EMA-Stichprobenvergleiche (d = 0.88)

1 Vergleich von Klassifikationsmethoden in simulierten EMA-Daten

“EMA_5.5” besteht aus je 5 MZP im Pre- und im Post-Intervall. Dies sind die ursprünglich simulierten EMA-Daten von N = 8040 Personen (ursprünglich N = 100.000).

“EMA_30.30” besteht aus je 30 MZP im Pre- und im Post-Intervall. Diese wurden aus den ursprünglichen Simulationsdaten erweitert und umfassen dieselben N = 8040 Personen.

“EMA_5.5_Window” besteht aus je 5 MZP im Pre- und im Post-Intervall, wobei diese (pro Person) jeweils als zusammenhängendes Intervall (Window) zufällig aus den Gesamt-Intervallen ausgewählt wurden. Die Stichprobe umfasst dieselben N = 8040 Personen.

“EMA_5.5_Days” besteht aus je 5 MZP im Pre- und im Post-Intervall, wobei diese pro Person jeweils unzusammenhängend zufällig aus den Gesamt-Intervallen ausgewählt wurden. Die Stichprobe umfasst dieselben N = 8040 Personen.

# Ausschluss von Personen ohne Varianz in min. einem MZP-Intervall

# sd(c(1,1,1,1,2)) = 0.4472136 = min. SD bei 5 (nicht gleichen) MZP
# sd(c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2)) = 0.1825742 = min. SD bei 30 (nicht gleichen) MZP

EMA_5.5 = EMA_5.5 %>% 
  filter(ind.pretestSD != 0 & ind.posttestSD != 0)

EMA_30.30 = EMA_30.30 %>% 
  filter(ind.pretestSD != 0 & ind.posttestSD != 0)


EMA_5.5 = EMA_5.5 %>% 
  filter(ID_orig %in% EMA_30.30$ID1_PRE)

EMA_30.30 = EMA_30.30 %>% 
  filter(ID1_PRE %in% EMA_5.5$ID_orig)

EMA_5.5 = EMA_5.5 %>% 
  add_column(., .before = "ID_orig", ID = 1:nrow(.))

EMA_30.30 = EMA_30.30 %>% 
  add_column(., .before = "ID1_PRE", ID = 1:nrow(.))

load("cor_04_k20/EMA_5.5_Window.RData")
load("cor_04_k20/EMA_5.5_Days.RData")

EMA_5.5_Window$PRE_Mean = apply(EMA_5.5_Window[pre_5mzp], 1, mean)
EMA_5.5_Window$POST_Mean = apply(EMA_5.5_Window[post_5mzp], 1, mean)
EMA_5.5_Window$MeanDiff = EMA_5.5_Window$PRE_Mean - EMA_5.5_Window$POST_Mean
EMA_5.5_Window$ind.pretestSD = apply(EMA_5.5_Window[pre_5mzp], 1, sd)
EMA_5.5_Window$ind.posttestSD = apply(EMA_5.5_Window[post_5mzp], 1, sd)

EMA_5.5_Days$PRE_Mean = apply(EMA_5.5_Days[pre_5mzp], 1, mean)
EMA_5.5_Days$POST_Mean = apply(EMA_5.5_Days[post_5mzp], 1, mean)
EMA_5.5_Days$MeanDiff = EMA_5.5_Days$PRE_Mean - EMA_5.5_Days$POST_Mean
EMA_5.5_Days$ind.pretestSD = apply(EMA_5.5_Days[pre_5mzp], 1, sd)
EMA_5.5_Days$ind.posttestSD = apply(EMA_5.5_Days[post_5mzp], 1, sd)

# Ausschluss von Personen ohne Varianz in min. einem MZP-Intervall

EMA_5.5_Window = EMA_5.5_Window %>% 
  filter(ind.pretestSD != 0 & ind.posttestSD != 0)

EMA_5.5_Days = EMA_5.5_Days %>% 
  filter(ind.pretestSD != 0 & ind.posttestSD != 0)

EMA_5.5 = EMA_5.5 %>% 
  filter(ID %in% EMA_30.30$ID & ID %in% EMA_5.5_Window$ID & ID %in% EMA_5.5_Days$ID)

EMA_30.30 = EMA_30.30 %>% 
  filter(ID %in% EMA_5.5$ID & ID %in% EMA_5.5_Window$ID & ID %in% EMA_5.5_Days$ID)

EMA_5.5_Window = EMA_5.5_Window %>% 
  filter(ID %in% EMA_5.5$ID & ID %in% EMA_30.30$ID & ID %in% EMA_5.5_Days$ID)

EMA_5.5_Days = EMA_5.5_Days %>% 
  filter(ID %in% EMA_5.5$ID & ID %in% EMA_30.30$ID & ID %in% EMA_5.5_Window$ID)

EMA_5.5$ID = 1:nrow(EMA_5.5)
EMA_30.30$ID = 1:nrow(EMA_30.30)
EMA_5.5_Window$ID = 1:nrow(EMA_5.5_Window)
EMA_5.5_Days$ID = 1:nrow(EMA_5.5_Days)

---

1.1 Überblick über die simulierten Daten

Beispiel-Verläufe in den 4 untersuchten Datensets

1.1.1 Original-Simulationsdaten (je 5 MZP)

EMA_5.5 %>%
  within(., {ind.pretestSD = round(ind.pretestSD, digits = 2)
            ind.posttestSD = round(ind.posttestSD, digits = 2)}) %>% 
  head() %>% 
  kable() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>% 
  scroll_box(width = "100%")

ID	ID_orig	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	PRE_Mean	POST_Mean	MeanDiff	ind.pretestSD	ind.posttestSD
1	1	9	8	14	10	17	5	2	2	6	3	11.6	3.6	8.0	3.78	1.82
2	3	8	9	11	12	7	5	4	5	7	2	9.4	4.6	4.8	2.07	1.82
3	4	11	10	5	7	5	18	7	9	5	14	7.6	10.6	-3.0	2.79	5.32
4	5	12	7	14	12	12	10	12	6	6	7	11.4	8.2	3.2	2.61	2.68
5	6	12	12	14	8	9	1	1	8	13	8	11.0	6.2	4.8	2.45	5.17
6	7	8	15	8	8	8	3	4	4	6	11	9.4	5.6	3.8	3.13	3.21

Pre-Post-Verläufe für 9 zufällig gezogene Personen

rand = sample(EMA_5.5$ID, 9)

x = tibble(ID = c(rep(rand[1],times=11),
                  rep(rand[2],times=11),
                  rep(rand[3],times=11),
                  rep(rand[4],times=11),
                  rep(rand[5],times=11),
                  rep(rand[6],times=11),
                  rep(rand[7],times=11),
                  rep(rand[8],times=11),
                  rep(rand[9],times=11)),
           MZP = rep(seq(as.Date("2020-01-01"), length.out=11, by="1 day"), times=9),
           Score = c(as.numeric(EMA_5.5[rand[1],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[1],post_5mzp]),
                     as.numeric(EMA_5.5[rand[2],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[2],post_5mzp]),
                     as.numeric(EMA_5.5[rand[3],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[3],post_5mzp]),
                     as.numeric(EMA_5.5[rand[4],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[4],post_5mzp]),
                     as.numeric(EMA_5.5[rand[5],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[5],post_5mzp]),
                     as.numeric(EMA_5.5[rand[6],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[6],post_5mzp]),
                     as.numeric(EMA_5.5[rand[7],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[7],post_5mzp]),
                     as.numeric(EMA_5.5[rand[8],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[8],post_5mzp]),
                     as.numeric(EMA_5.5[rand[9],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[9],post_5mzp])))

x %>%
  group_by(ID) %>% 
  plot_time_series(MZP, Score,
    #.color_var = ID,           # for multiple lines in one plot
    #.color_lab = "ID",
    .facet_ncol = 3,
    .facet_scales = "fixed",
    .interactive = TRUE,
    .facet_collapse = FALSE,
    .smooth = TRUE,
    .smooth_degree = 2,
    .smooth_alpha = 0.5,
    .smooth_size = 0.2
  )

# don´t run this section (code for extremely computation-intense plots that I already stored as .RData and .jpg)
# repeated-measures scatter-boxplot-violin-histograms for individual PRE and POST means
# from van Langen (2020) Open-visualizations tutorial for repeated measures in R

# EMA_5.5
# converting my dataframes to use in the same ggplot structure:
EMA_5.5_ts = EMA_5.5 %>% 
  select(ID, PRE_Mean, POST_Mean) %>% 
  pivot_longer(!ID, names_to = "Interval", values_to = "Mean") %>% 
  mutate(ID = as.factor(ID),
         Interval = rep(c(1,2), times = nrow(EMA_5.5)))

save(EMA_5.5_ts, file = "Time Series Dataframes/k20_EMA_5.5_ts.RData")

###

load("Time Series Dataframes/k20_EMA_5.5_ts.RData")

# Repeated measures with box− and violin plots
EMA_5.5_ts$jit = jitter(EMA_5.5_ts$Interval, amount = .09)

Pre_Post_Box_Violin = ggplot(data = EMA_5.5_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .5) +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .5) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.25),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "dodgerblue", alpha = .5) +
  geom_half_boxplot(
    data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .15),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "darkorange", alpha = .5) +
  geom_half_violin(
    data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = 1.3),
    side = "r", fill = "dodgerblue", alpha = .5, trim = FALSE) +
  geom_half_violin(
    data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange", alpha = .5, trim = FALSE) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoints): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_Pre-Post_Box_Violin.jpg", plot = Pre_Post_Box_Violin, width = 6, height = 4)
save(Pre_Post_Box_Violin, file = "Time Series Dataframes/k20_EMA_5.5_Pre_Post_Box_Violin.RData")


# Repeated measures with box− and violin plots and means + CIs
score_mean_1 = EMA_5.5_ts %>% filter(Interval == "1") %>% summarise(mean(Mean)) %>% as.numeric()
score_mean_2 = EMA_5.5_ts %>% filter(Interval == "2") %>% summarise(mean(Mean)) %>% as.numeric()
score_median1 = EMA_5.5_ts %>% filter(Interval == "1") %>% summarise(median(Mean)) %>% as.numeric()
score_median2 = EMA_5.5_ts %>% filter(Interval == "2") %>% summarise(median(Mean)) %>% as.numeric()
score_sd_1 = EMA_5.5_ts %>% filter(Interval == "1") %>% summarise(sd(Mean)) %>% as.numeric()
score_sd_2 = EMA_5.5_ts %>% filter(Interval == "2") %>% summarise(sd(Mean)) %>% as.numeric()
score_se_1 = score_sd_1/sqrt(nrow(EMA_5.5))
score_se_2 = score_sd_2/sqrt(nrow(EMA_5.5))
score_ci_1 = EMA_5.5_ts %>% filter(Interval == "1") %>% pull(Mean) %>% CI(., ci = 0.95)
score_ci_2 = EMA_5.5_ts %>% filter(Interval == "2") %>% pull(Mean) %>% CI(., ci = 0.95)
#Create data frame with 2 rows and 7 columns containing the descriptives
group = c("PRE", "POST")
N = c(nrow(EMA_5.5), nrow(EMA_5.5))
score_mean = c(score_mean_1, score_mean_2)
score_median = c(score_median1, score_median2)
sd = c(score_sd_1, score_sd_2)
se = c(score_se_1, score_se_2)
ci = c(as.numeric(score_ci_1[1] - score_ci_1[3]), as.numeric(score_ci_2[1] - score_ci_2[3]))
summary_df = data.frame(group, N, score_mean, score_median, sd, se, ci)

# EMA_5.5_ts$jit = jitter(EMA_5.5_ts$Interval, amount = .09)     #already created above
x_tick_means = c(.87, 2.13)

Pre_Post_Box_Violin_Mean_CI = ggplot(data = EMA_5.5_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .6) +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .6) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.28),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "dodgerblue") +
  geom_half_boxplot(
    data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .18),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "darkorange") +
  geom_half_violin(
    data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.3),
    side = "l", fill = "dodgerblue") +
  geom_half_violin(
    data = EMA_5.5_ts %>% filter(Interval == "2"),aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange") +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1]),
             position = position_nudge(x = -.13), color = "dodgerblue", alpha = .6, size = 1.5) +
  geom_errorbar(data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1],
                                                 ymin = score_mean[1]-ci[1], ymax = score_mean[1]+ci[1]),
                position = position_nudge(-.13), color = "dodgerblue", width = 0.05, size = 0.4, alpha = .6) +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2]),
             position = position_nudge(x = .13), color = "darkorange", alpha = .6, size = 1.5)+
  geom_errorbar(data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2],
                                                 ymin = score_mean[2]-ci[2], ymax = score_mean[2]+ci[2]), 
                position = position_nudge(.13), color = "darkorange", width = 0.05, size = 0.4, alpha = .6) +
  geom_line(data = summary_df, aes(x = x_tick_means, y = score_mean), color = "gray", size = 1) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoints): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_Pre-Post_Box_Violin_Mean+CI.jpg", plot = Pre_Post_Box_Violin_Mean_CI, width = 6, height = 4)
save(Pre_Post_Box_Violin_Mean_CI, file = "Time Series Dataframes/k20_EMA_5.5_Pre_Post_Box_Violin_Mean_CI.RData")

#knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_Pre-Post_Box_Violin.jpg")
knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_Pre-Post_Box_Violin_Mean+CI.jpg")

---

1.1.2 Erweiterte Intervall-Daten (je 30 MZP)

EMA_30.30 %>% 
  select(-(ID1_PRE:ID6_POST)) %>% 
  within(., {ind.pretestSD = round(ind.pretestSD, digits = 2)
            ind.posttestSD = round(ind.posttestSD, digits = 2)}) %>% 
  head() %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>% 
  scroll_box(width = "100%")

ID	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	PRE1_6	PRE1_7	PRE1_8	PRE1_9	PRE1_10	PRE1_11	PRE1_12	PRE1_13	PRE1_14	PRE1_15	PRE1_16	PRE1_17	PRE1_18	PRE1_19	PRE1_20	PRE1_21	PRE1_22	PRE1_23	PRE1_24	PRE1_25	PRE1_26	PRE1_27	PRE1_28	PRE1_29	PRE1_30	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	POST1_6	POST1_7	POST1_8	POST1_9	POST1_10	POST1_11	POST1_12	POST1_13	POST1_14	POST1_15	POST1_16	POST1_17	POST1_18	POST1_19	POST1_20	POST1_21	POST1_22	POST1_23	POST1_24	POST1_25	POST1_26	POST1_27	POST1_28	POST1_29	POST1_30	PRE_Mean	POST_Mean	MeanDiff	ind.pretestSD	ind.posttestSD
1	9	8	14	10	17	11	11	10	18	8	7	8	14	15	14	9	8	10	14	17	8	14	14	15	7	11	14	16	11	6	5	2	2	6	3	2	5	3	2	6	4	4	1	6	3	3	4	4	6	1	3	2	2	6	5	3	4	1	4	6	11.6	3.6	8.0	3.44	1.65
2	8	9	11	12	7	11	10	11	9	6	11	9	12	8	7	9	12	11	8	7	11	7	8	9	12	12	9	8	11	7	5	4	5	7	2	6	3	7	4	3	6	4	3	7	3	3	4	7	6	3	6	7	3	4	3	7	2	5	4	5	9.4	4.6	4.8	1.89	1.65
3	11	10	5	7	5	9	10	9	7	3	9	10	9	7	3	5	10	11	7	5	10	7	5	5	11	7	10	9	9	3	18	7	9	5	14	8	3	16	11	15	3	8	15	11	16	12	8	5	19	9	16	8	15	11	3	11	18	5	6	13	7.6	10.6	-3.0	2.54	4.84
4	12	7	14	12	12	10	12	8	12	15	10	10	16	11	10	13	9	11	15	9	10	16	10	11	10	11	10	10	16	10	10	12	6	6	7	12	10	6	6	7	8	11	10	8	4	12	6	6	7	10	11	5	7	7	11	7	10	10	10	4	11.4	8.2	3.2	2.37	2.44
5	12	12	14	8	9	8	9	12	14	12	13	14	10	10	8	14	10	13	8	10	13	11	7	11	13	7	11	13	13	11	1	1	8	13	8	14	9	3	3	2	3	15	5	2	6	10	5	1	2	13	2	15	6	5	3	3	3	2	9	14	11.0	6.2	4.8	2.23	4.70
6	8	15	8	8	8	14	10	10	7	6	11	14	8	6	8	10	10	12	11	4	14	11	6	8	8	14	10	10	7	6	3	4	4	6	11	6	4	4	3	11	4	6	9	1	8	1	6	8	9	4	8	6	4	9	1	10	3	4	8	3	9.4	5.6	3.8	2.85	2.92

Pre-Post-Verläufe für 9 zufällig gezogene Personen

rand = sample(EMA_30.30$ID, 9)

x = tibble(ID = c(rep(rand[1],times=61),
                     rep(rand[2],times=61),
                     rep(rand[3],times=61),
                     rep(rand[4],times=61),
                     rep(rand[5],times=61),
                     rep(rand[6],times=61),
                     rep(rand[7],times=61),
                     rep(rand[8],times=61),
                     rep(rand[9],times=61)),
              MZP = rep(seq(as.Date("2020-01-01"), length.out=61, by="1 day"), times=9),
              Score = c(as.numeric(EMA_30.30[rand[1],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[1],post_30mzp]),
                        as.numeric(EMA_30.30[rand[2],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[2],post_30mzp]),
                        as.numeric(EMA_30.30[rand[3],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[3],post_30mzp]),
                        as.numeric(EMA_30.30[rand[4],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[4],post_30mzp]),
                        as.numeric(EMA_30.30[rand[5],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[5],post_30mzp]),
                        as.numeric(EMA_30.30[rand[6],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[6],post_30mzp]),
                        as.numeric(EMA_30.30[rand[7],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[7],post_30mzp]),
                        as.numeric(EMA_30.30[rand[8],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[8],post_30mzp]),
                        as.numeric(EMA_30.30[rand[9],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[9],post_30mzp])))

x %>%
  group_by(ID) %>% 
  plot_time_series(MZP, Score,
    #.color_var = ID,           # for multiple lines in one plot
    #.color_lab = "ID",
    .facet_ncol = 3,
    .facet_scales = "fixed",
    .interactive = TRUE,
    .facet_collapse = FALSE,
    .smooth = TRUE,
    .smooth_degree = 2,
    .smooth_alpha = 0.5,
    .smooth_size = 0.2
  )

# don´t run this section (code for extremely computation-intense plots that I already stored as .RData and .jpg)
# repeated-measures scatter-boxplot-violin-histograms for individual PRE and POST means
# from van Langen (2020) Open-visualizations tutorial for repeated measures in R

# EMA_30.30
# converting my dataframes to use in the same ggplot structure:
EMA_30.30_ts = EMA_30.30 %>% 
  select(ID, PRE_Mean, POST_Mean) %>% 
  pivot_longer(!ID, names_to = "Interval", values_to = "Mean") %>% 
  mutate(ID = as.factor(ID),
         Interval = rep(c(1,2), times = nrow(EMA_30.30)))

save(EMA_30.30_ts, file = "Time Series Dataframes/k20_EMA_30.30_ts.RData")

###

load("Time Series Dataframes/k20_EMA_30.30_ts.RData")

# Repeated measures with box− and violin plots
EMA_30.30_ts$jit = jitter(EMA_30.30_ts$Interval, amount = .09)

Pre_Post_Box_Violin = ggplot(data = EMA_30.30_ts, aes(y = Mean)) +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .5) +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .5) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.25),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "dodgerblue", alpha = .5) +
  geom_half_boxplot(
    data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .15),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "darkorange", alpha = .5) +
  geom_half_violin(
    data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = 1.3),
    side = "r", fill = "dodgerblue", alpha = .5, trim = FALSE) +
  geom_half_violin(
    data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange", alpha = .5, trim = FALSE) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (30+30 Timepoints): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_30.30_Pre-Post_Box_Violin.jpg", plot = Pre_Post_Box_Violin, width = 6, height = 4)
save(Pre_Post_Box_Violin, file = "Time Series Dataframes/k20_EMA_30.30_Pre_Post_Box_Violin.RData")


# Repeated measures with box− and violin plots and means + CIs
score_mean_1 = EMA_30.30_ts %>% filter(Interval == "1") %>% summarise(mean(Mean)) %>% as.numeric()
score_mean_2 = EMA_30.30_ts %>% filter(Interval == "2") %>% summarise(mean(Mean)) %>% as.numeric()
score_median1 = EMA_30.30_ts %>% filter(Interval == "1") %>% summarise(median(Mean)) %>% as.numeric()
score_median2 = EMA_30.30_ts %>% filter(Interval == "2") %>% summarise(median(Mean)) %>% as.numeric()
score_sd_1 = EMA_30.30_ts %>% filter(Interval == "1") %>% summarise(sd(Mean)) %>% as.numeric()
score_sd_2 = EMA_30.30_ts %>% filter(Interval == "2") %>% summarise(sd(Mean)) %>% as.numeric()
score_se_1 = score_sd_1/sqrt(nrow(EMA_30.30))
score_se_2 = score_sd_2/sqrt(nrow(EMA_30.30))
score_ci_1 = EMA_30.30_ts %>% filter(Interval == "1") %>% pull(Mean) %>% CI(., ci = 0.95)
score_ci_2 = EMA_30.30_ts %>% filter(Interval == "2") %>% pull(Mean) %>% CI(., ci = 0.95)
#Create data frame with 2 rows and 7 columns containing the descriptives
group = c("PRE", "POST")
N = c(nrow(EMA_30.30), nrow(EMA_30.30))
score_mean = c(score_mean_1, score_mean_2)
score_median = c(score_median1, score_median2)
sd = c(score_sd_1, score_sd_2)
se = c(score_se_1, score_se_2)
ci = c(as.numeric(score_ci_1[1] - score_ci_1[3]), as.numeric(score_ci_2[1] - score_ci_2[3]))
summary_df = data.frame(group, N, score_mean, score_median, sd, se, ci)

# EMA_30.30_ts$jit = jitter(EMA_30.30_ts$Interval, amount = .09)     #already created above
x_tick_means = c(.87, 2.13)

Pre_Post_Box_Violin_Mean_CI = ggplot(data = EMA_30.30_ts, aes(y = Mean)) +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .6) +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .6) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.28),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "dodgerblue") +
  geom_half_boxplot(
    data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .18),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "darkorange") +
  geom_half_violin(
    data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.3),
    side = "l", fill = "dodgerblue") +
  geom_half_violin(
    data = EMA_30.30_ts %>% filter(Interval == "2"),aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange") +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1]),
             position = position_nudge(x = -.13), color = "dodgerblue", alpha = .6, size = 1.5) +
  geom_errorbar(data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1],
                                                 ymin = score_mean[1]-ci[1], ymax = score_mean[1]+ci[1]),
                position = position_nudge(-.13), color = "dodgerblue", width = 0.05, size = 0.4, alpha = .6) +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2]),
             position = position_nudge(x = .13), color = "darkorange", alpha = .6, size = 1.5)+
  geom_errorbar(data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2],
                                                 ymin = score_mean[2]-ci[2], ymax = score_mean[2]+ci[2]), 
                position = position_nudge(.13), color = "darkorange", width = 0.05, size = 0.4, alpha = .6) +
  geom_line(data = summary_df, aes(x = x_tick_means, y = score_mean), color = "gray", size = 1) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (30+30 Timepoints): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_30.30_Pre-Post_Box_Violin_Mean+CI.jpg", plot = Pre_Post_Box_Violin_Mean_CI, width = 6, height = 4)
save(Pre_Post_Box_Violin_Mean_CI, file = "Time Series Dataframes/k20_EMA_30.30_Pre_Post_Box_Violin_Mean_CI.RData")

#knitr::include_graphics("Time Series Dataframes/k20_EMA_30.30_Pre-Post_Box_Violin.jpg")
knitr::include_graphics("Time Series Dataframes/k20_EMA_30.30_Pre-Post_Box_Violin_Mean+CI.jpg")

---

1.1.3 Zufallsauswahl: Random Window (je 5 MZP)

EMA_5.5_Window %>%
  within(., {ind.pretestSD = round(ind.pretestSD, digits = 2)
            ind.posttestSD = round(ind.posttestSD, digits = 2)}) %>% 
  head() %>% 
  kable() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>% 
  scroll_box(width = "100%")

ID	Pre_MZP1	Pre_MZP2	Pre_MZP3	Pre_MZP4	Pre_MZP5	Post_MZP1	Post_MZP2	Post_MZP3	Post_MZP4	Post_MZP5	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	PRE_Mean	POST_Mean	MeanDiff	ind.pretestSD	ind.posttestSD
1	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_25	POST1_26	POST1_27	POST1_28	POST1_29	9	8	14	10	17	5	3	4	1	4	11.6	3.4	8.2	3.78	1.52
2	PRE1_10	PRE1_11	PRE1_12	PRE1_13	PRE1_14	POST1_4	POST1_5	POST1_6	POST1_7	POST1_8	6	11	9	12	8	7	2	6	3	7	9.2	5.0	4.2	2.39	2.35
3	PRE1_18	PRE1_19	PRE1_20	PRE1_21	PRE1_22	POST1_26	POST1_27	POST1_28	POST1_29	POST1_30	11	7	5	10	7	11	18	5	6	13	8.0	10.6	-2.6	2.45	5.32
4	PRE1_17	PRE1_18	PRE1_19	PRE1_20	PRE1_21	POST1_15	POST1_16	POST1_17	POST1_18	POST1_19	9	11	15	9	10	4	12	6	6	7	10.8	7.0	3.8	2.49	3.00
5	PRE1_24	PRE1_25	PRE1_26	PRE1_27	PRE1_28	POST1_7	POST1_8	POST1_9	POST1_10	POST1_11	11	13	7	11	13	9	3	3	2	3	11.0	4.0	7.0	2.45	2.83
6	PRE1_4	PRE1_5	PRE1_6	PRE1_7	PRE1_8	POST1_25	POST1_26	POST1_27	POST1_28	POST1_29	8	8	14	10	10	1	10	3	4	8	10.0	5.2	4.8	2.45	3.70

Pre-Post-Verläufe für 9 zufällig gezogene Personen

rand = sample(EMA_5.5_Window$ID, 9)

x = tibble(ID = c(rep(rand[1],times=11),
                  rep(rand[2],times=11),
                  rep(rand[3],times=11),
                  rep(rand[4],times=11),
                  rep(rand[5],times=11),
                  rep(rand[6],times=11),
                  rep(rand[7],times=11),
                  rep(rand[8],times=11),
                  rep(rand[9],times=11)),
           MZP = rep(seq(as.Date("2020-01-01"), length.out=11, by="1 day"), times=9),
           Score = c(as.numeric(EMA_5.5_Window[rand[1],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[1],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[2],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[2],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[3],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[3],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[4],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[4],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[5],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[5],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[6],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[6],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[7],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[7],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[8],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[8],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[9],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[9],post_5mzp])))

x %>%
  group_by(ID) %>% 
  plot_time_series(MZP, Score,
    #.color_var = ID,           # for multiple lines in one plot
    #.color_lab = "ID",
    .facet_ncol = 3,
    .facet_scales = "fixed",
    .interactive = TRUE,
    .facet_collapse = FALSE,
    .smooth = TRUE,
    .smooth_degree = 2,
    .smooth_alpha = 0.5,
    .smooth_size = 0.2
  )

# don´t run this section (code for extremely computation-intense plots that I already stored as .RData and .jpg)
# repeated-measures scatter-boxplot-violin-histograms for individual PRE and POST means
# from van Langen (2020) Open-visualizations tutorial for repeated measures in R

# EMA_5.5_Window
# converting my dataframes to use in the same ggplot structure:
EMA_5.5_Window_ts = EMA_5.5_Window %>% 
  select(ID, PRE_Mean, POST_Mean) %>% 
  pivot_longer(!ID, names_to = "Interval", values_to = "Mean") %>% 
  mutate(ID = as.factor(ID),
         Interval = rep(c(1,2), times = nrow(EMA_5.5_Window)))

save(EMA_5.5_Window_ts, file = "Time Series Dataframes/k20_EMA_5.5_Window_ts.RData")

###

load("Time Series Dataframes/k20_EMA_5.5_Window_ts.RData")

# Repeated measures with box− and violin plots
EMA_5.5_Window_ts$jit = jitter(EMA_5.5_Window_ts$Interval, amount = .09)

Pre_Post_Box_Violin = ggplot(data = EMA_5.5_Window_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .5) +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .5) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.25),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "dodgerblue", alpha = .5) +
  geom_half_boxplot(
    data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .15),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "darkorange", alpha = .5) +
  geom_half_violin(
    data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = 1.3),
    side = "r", fill = "dodgerblue", alpha = .5, trim = FALSE) +
  geom_half_violin(
    data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange", alpha = .5, trim = FALSE) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoint Random Windows): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_Window_Pre-Post_Box_Violin.jpg", plot = Pre_Post_Box_Violin, width = 6, height = 4)
save(Pre_Post_Box_Violin, file = "Time Series Dataframes/k20_EMA_5.5_Window_Pre_Post_Box_Violin.RData")


# Repeated measures with box− and violin plots and means + CIs
score_mean_1 = EMA_5.5_Window_ts %>% filter(Interval == "1") %>% summarise(mean(Mean)) %>% as.numeric()
score_mean_2 = EMA_5.5_Window_ts %>% filter(Interval == "2") %>% summarise(mean(Mean)) %>% as.numeric()
score_median1 = EMA_5.5_Window_ts %>% filter(Interval == "1") %>% summarise(median(Mean)) %>% as.numeric()
score_median2 = EMA_5.5_Window_ts %>% filter(Interval == "2") %>% summarise(median(Mean)) %>% as.numeric()
score_sd_1 = EMA_5.5_Window_ts %>% filter(Interval == "1") %>% summarise(sd(Mean)) %>% as.numeric()
score_sd_2 = EMA_5.5_Window_ts %>% filter(Interval == "2") %>% summarise(sd(Mean)) %>% as.numeric()
score_se_1 = score_sd_1/sqrt(nrow(EMA_5.5_Window))
score_se_2 = score_sd_2/sqrt(nrow(EMA_5.5_Window))
score_ci_1 = EMA_5.5_Window_ts %>% filter(Interval == "1") %>% pull(Mean) %>% CI(., ci = 0.95)
score_ci_2 = EMA_5.5_Window_ts %>% filter(Interval == "2") %>% pull(Mean) %>% CI(., ci = 0.95)
#Create data frame with 2 rows and 7 columns containing the descriptives
group = c("PRE", "POST")
N = c(nrow(EMA_5.5_Window), nrow(EMA_5.5_Window))
score_mean = c(score_mean_1, score_mean_2)
score_median = c(score_median1, score_median2)
sd = c(score_sd_1, score_sd_2)
se = c(score_se_1, score_se_2)
ci = c(as.numeric(score_ci_1[1] - score_ci_1[3]), as.numeric(score_ci_2[1] - score_ci_2[3]))
summary_df = data.frame(group, N, score_mean, score_median, sd, se, ci)

# EMA_5.5_Window_ts$jit = jitter(EMA_5.5_Window_ts$Interval, amount = .09)     #already created above
x_tick_means = c(.87, 2.13)

Pre_Post_Box_Violin_Mean_CI = ggplot(data = EMA_5.5_Window_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .6) +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .6) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.28),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "dodgerblue") +
  geom_half_boxplot(
    data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .18),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "darkorange") +
  geom_half_violin(
    data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.3),
    side = "l", fill = "dodgerblue") +
  geom_half_violin(
    data = EMA_5.5_Window_ts %>% filter(Interval == "2"),aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange") +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1]),
             position = position_nudge(x = -.13), color = "dodgerblue", alpha = .6, size = 1.5) +
  geom_errorbar(data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1],
                                                 ymin = score_mean[1]-ci[1], ymax = score_mean[1]+ci[1]),
                position = position_nudge(-.13), color = "dodgerblue", width = 0.05, size = 0.4, alpha = .6) +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2]),
             position = position_nudge(x = .13), color = "darkorange", alpha = .6, size = 1.5)+
  geom_errorbar(data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2],
                                                 ymin = score_mean[2]-ci[2], ymax = score_mean[2]+ci[2]), 
                position = position_nudge(.13), color = "darkorange", width = 0.05, size = 0.4, alpha = .6) +
  geom_line(data = summary_df, aes(x = x_tick_means, y = score_mean), color = "gray", size = 1) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoint Random Windows): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_Window_Pre-Post_Box_Violin_Mean+CI.jpg", plot = Pre_Post_Box_Violin_Mean_CI, width = 6, height = 4)
save(Pre_Post_Box_Violin_Mean_CI, file = "Time Series Dataframes/k20_EMA_5.5_Window_Pre_Post_Box_Violin_Mean_CI.RData")

#knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_Window_Pre-Post_Box_Violin.jpg")
knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_Window_Pre-Post_Box_Violin_Mean+CI.jpg")

---

1.1.4 Zufallsauswahl: Random Days (je 5 MZP)

EMA_5.5_Days %>%
  within(., {ind.pretestSD = round(ind.pretestSD, digits = 2)
            ind.posttestSD = round(ind.posttestSD, digits = 2)}) %>% 
  head() %>% 
  kable() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>% 
  scroll_box(width = "100%")

ID	Pre_MZP1	Pre_MZP2	Pre_MZP3	Pre_MZP4	Pre_MZP5	Post_MZP1	Post_MZP2	Post_MZP3	Post_MZP4	Post_MZP5	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	PRE_Mean	POST_Mean	MeanDiff	ind.pretestSD	ind.posttestSD
1	PRE1_1	PRE1_5	PRE1_10	PRE1_17	PRE1_25	POST1_4	POST1_15	POST1_17	POST1_18	POST1_26	9	17	8	8	7	6	3	4	4	3	9.8	4.0	5.8	4.09	1.22
2	PRE1_4	PRE1_5	PRE1_7	PRE1_24	PRE1_25	POST1_14	POST1_15	POST1_18	POST1_20	POST1_26	12	7	10	9	12	7	3	7	3	7	10.0	5.4	4.6	2.12	2.19
3	PRE1_3	PRE1_4	PRE1_9	PRE1_25	PRE1_27	POST1_2	POST1_5	POST1_13	POST1_20	POST1_30	5	7	7	11	10	7	14	15	9	13	8.0	11.6	-3.6	2.45	3.44
4	PRE1_1	PRE1_3	PRE1_8	PRE1_26	PRE1_28	POST1_10	POST1_11	POST1_15	POST1_22	POST1_24	12	14	8	11	10	7	8	4	5	7	11.0	6.2	4.8	2.24	1.64
5	PRE1_4	PRE1_8	PRE1_22	PRE1_26	PRE1_28	POST1_4	POST1_5	POST1_13	POST1_18	POST1_28	8	12	11	7	13	13	8	5	1	2	10.2	5.8	4.4	2.59	4.87
6	PRE1_2	PRE1_3	PRE1_18	PRE1_24	PRE1_29	POST1_17	POST1_18	POST1_21	POST1_23	POST1_26	15	8	12	8	7	6	8	8	4	10	10.0	7.2	2.8	3.39	2.28

Pre-Post-Verläufe für 9 zufällig gezogene Personen

rand = sample(EMA_5.5_Days$ID, 9)

x = tibble(ID = c(rep(rand[1],times=11),
                  rep(rand[2],times=11),
                  rep(rand[3],times=11),
                  rep(rand[4],times=11),
                  rep(rand[5],times=11),
                  rep(rand[6],times=11),
                  rep(rand[7],times=11),
                  rep(rand[8],times=11),
                  rep(rand[9],times=11)),
           MZP = rep(seq(as.Date("2020-01-01"), length.out=11, by="1 day"), times=9),
           Score = c(as.numeric(EMA_5.5_Days[rand[1],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[1],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[2],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[2],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[3],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[3],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[4],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[4],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[5],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[5],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[6],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[6],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[7],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[7],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[8],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[8],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[9],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[9],post_5mzp])))

x %>%
  group_by(ID) %>% 
  plot_time_series(MZP, Score,
    #.color_var = ID,           # for multiple lines in one plot
    #.color_lab = "ID",
    .facet_ncol = 3,
    .facet_scales = "fixed",
    .interactive = TRUE,
    .facet_collapse = FALSE,
    .smooth = TRUE,
    .smooth_degree = 2,
    .smooth_alpha = 0.5,
    .smooth_size = 0.2
  )

# don´t run this section (code for extremely computation-intense plots that I already stored as .RData and .jpg)
# repeated-measures scatter-boxplot-violin-histograms for individual PRE and POST means
# from van Langen (2020) Open-visualizations tutorial for repeated measures in R

# EMA_5.5_Days
# converting my dataframes to use in the same ggplot structure:
EMA_5.5_Days_ts = EMA_5.5_Days %>% 
  select(ID, PRE_Mean, POST_Mean) %>% 
  pivot_longer(!ID, names_to = "Interval", values_to = "Mean") %>% 
  mutate(ID = as.factor(ID),
         Interval = rep(c(1,2), times = nrow(EMA_5.5_Days)))

save(EMA_5.5_Days_ts, file = "Time Series Dataframes/k20_EMA_5.5_Days_ts.RData")

###

load("Time Series Dataframes/k20_EMA_5.5_Days_ts.RData")

# Repeated measures with box− and violin plots
EMA_5.5_Days_ts$jit = jitter(EMA_5.5_Days_ts$Interval, amount = .09)

Pre_Post_Box_Violin = ggplot(data = EMA_5.5_Days_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .5) +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .5) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.25),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "dodgerblue", alpha = .5) +
  geom_half_boxplot(
    data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .15),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "darkorange", alpha = .5) +
  geom_half_violin(
    data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = 1.3),
    side = "r", fill = "dodgerblue", alpha = .5, trim = FALSE) +
  geom_half_violin(
    data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange", alpha = .5, trim = FALSE) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoint Random Days): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_Days_Pre-Post_Box_Violin.jpg", plot = Pre_Post_Box_Violin, width = 6, height = 4)
save(Pre_Post_Box_Violin, file = "Time Series Dataframes/k20_EMA_5.5_Days_Pre_Post_Box_Violin.RData")


# Repeated measures with box− and violin plots and means + CIs
score_mean_1 = EMA_5.5_Days_ts %>% filter(Interval == "1") %>% summarise(mean(Mean)) %>% as.numeric()
score_mean_2 = EMA_5.5_Days_ts %>% filter(Interval == "2") %>% summarise(mean(Mean)) %>% as.numeric()
score_median1 = EMA_5.5_Days_ts %>% filter(Interval == "1") %>% summarise(median(Mean)) %>% as.numeric()
score_median2 = EMA_5.5_Days_ts %>% filter(Interval == "2") %>% summarise(median(Mean)) %>% as.numeric()
score_sd_1 = EMA_5.5_Days_ts %>% filter(Interval == "1") %>% summarise(sd(Mean)) %>% as.numeric()
score_sd_2 = EMA_5.5_Days_ts %>% filter(Interval == "2") %>% summarise(sd(Mean)) %>% as.numeric()
score_se_1 = score_sd_1/sqrt(nrow(EMA_5.5_Days))
score_se_2 = score_sd_2/sqrt(nrow(EMA_5.5_Days))
score_ci_1 = EMA_5.5_Days_ts %>% filter(Interval == "1") %>% pull(Mean) %>% CI(., ci = 0.95)
score_ci_2 = EMA_5.5_Days_ts %>% filter(Interval == "2") %>% pull(Mean) %>% CI(., ci = 0.95)
#Create data frame with 2 rows and 7 columns containing the descriptives
group = c("PRE", "POST")
N = c(nrow(EMA_5.5_Days), nrow(EMA_5.5_Days))
score_mean = c(score_mean_1, score_mean_2)
score_median = c(score_median1, score_median2)
sd = c(score_sd_1, score_sd_2)
se = c(score_se_1, score_se_2)
ci = c(as.numeric(score_ci_1[1] - score_ci_1[3]), as.numeric(score_ci_2[1] - score_ci_2[3]))
summary_df = data.frame(group, N, score_mean, score_median, sd, se, ci)

# EMA_5.5_Days_ts$jit = jitter(EMA_5.5_Days_ts$Interval, amount = .09)     #already created above
x_tick_means = c(.87, 2.13)

Pre_Post_Box_Violin_Mean_CI = ggplot(data = EMA_5.5_Days_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .6) +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .6) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.28),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "dodgerblue") +
  geom_half_boxplot(
    data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .18),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "darkorange") +
  geom_half_violin(
    data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.3),
    side = "l", fill = "dodgerblue") +
  geom_half_violin(
    data = EMA_5.5_Days_ts %>% filter(Interval == "2"),aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange") +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1]),
             position = position_nudge(x = -.13), color = "dodgerblue", alpha = .6, size = 1.5) +
  geom_errorbar(data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1],
                                                 ymin = score_mean[1]-ci[1], ymax = score_mean[1]+ci[1]),
                position = position_nudge(-.13), color = "dodgerblue", width = 0.05, size = 0.4, alpha = .6) +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2]),
             position = position_nudge(x = .13), color = "darkorange", alpha = .6, size = 1.5)+
  geom_errorbar(data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2],
                                                 ymin = score_mean[2]-ci[2], ymax = score_mean[2]+ci[2]), 
                position = position_nudge(.13), color = "darkorange", width = 0.05, size = 0.4, alpha = .6) +
  geom_line(data = summary_df, aes(x = x_tick_means, y = score_mean), color = "gray", size = 1) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoint Random Days): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_Days_Pre-Post_Box_Violin_Mean+CI.jpg", plot = Pre_Post_Box_Violin_Mean_CI, width = 6, height = 4)
save(Pre_Post_Box_Violin_Mean_CI, file = "Time Series Dataframes/k20_EMA_5.5_Days_Pre_Post_Box_Violin_Mean_CI.RData")

#knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_Days_Pre-Post_Box_Violin.jpg")
knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_Days_Pre-Post_Box_Violin_Mean+CI.jpg")

---

1.2 Deskriptive Statistiken der Datensets

tibble(Descriptives = c("mean_PRE_Mean","mean_POST_Mean","mean_MeanDiff","mean_ind.pretestSD","mean_ind.posttestSD"),
       EMA_5.5 = round(c(mean(EMA_5.5$PRE_Mean),mean(EMA_5.5$POST_Mean),mean(EMA_5.5$MeanDiff),
                        mean(EMA_5.5$ind.pretestSD),mean(EMA_5.5$ind.posttestSD)), digits = 3),
       EMA_30.30 = round(c(mean(EMA_30.30$PRE_Mean),mean(EMA_30.30$POST_Mean),mean(EMA_30.30$MeanDiff),
                          mean(EMA_30.30$ind.pretestSD),mean(EMA_30.30$ind.posttestSD)), digits = 3),
       EMA_5.5_Window = round(c(mean(EMA_5.5_Window$PRE_Mean),mean(EMA_5.5_Window$POST_Mean),
                             mean(EMA_5.5_Window$MeanDiff),mean(EMA_5.5_Window$ind.pretestSD),
                             mean(EMA_5.5_Window$ind.posttestSD)), digits = 3),
       EMA_5.5_Days = round(c(mean(EMA_5.5_Days$PRE_Mean),mean(EMA_5.5_Days$POST_Mean),mean(EMA_5.5_Days$MeanDiff),
                           mean(EMA_5.5_Days$ind.pretestSD),mean(EMA_5.5_Days$ind.posttestSD)), digits = 3)) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Descriptives	EMA_5.5	EMA_30.30	EMA_5.5_Window	EMA_5.5_Days
mean_PRE_Mean	10.307	10.307	10.320	10.314
mean_POST_Mean	7.116	7.116	7.098	7.113
mean_MeanDiff	3.191	3.191	3.222	3.200
mean_ind.pretestSD	2.756	2.508	2.579	2.417
mean_ind.posttestSD	3.425	3.115	3.182	2.982

Boxplots der Pre- und Post-Mittelwerte

# ein Boxplot mit Pre- und Post-Verteilungen
#temp = tibble(Scores = c(EMA_5.5$PRE_Mean, EMA_5.5$POST_Mean, EMA_30.30$PRE_Mean, EMA_30.30$POST_Mean, 
#                         EMA_5.5_Window$PRE_Mean, EMA_5.5_Window$POST_Mean, EMA_5.5_Days$PRE_Mean, EMA_5.5_Days$POST_Mean),
#              Datasets = rep(as_factor(c("EMA_5.5", "EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days")), each = 2*length(EMA_5.5$PRE_Mean)),
#              Assessment = rep(as_factor(c("PRE", "POST", "PRE", "POST", "PRE", "POST", "PRE", "POST")), each = length(EMA_5.5$PRE_Mean)))#<<

temp = tibble(Scores = c(EMA_30.30$PRE_Mean, EMA_30.30$POST_Mean, EMA_5.5_Window$PRE_Mean, EMA_5.5_Window$POST_Mean, 
                         EMA_5.5_Days$PRE_Mean, EMA_5.5_Days$POST_Mean),
              Datasets = rep(as_factor(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days")), each = 2*length(EMA_30.30$PRE_Mean)),
              Assessment = rep(as_factor(c("PRE", "POST", "PRE", "POST", "PRE", "POST")), each = length(EMA_30.30$PRE_Mean)))#<<

ggplot(temp, aes(x = Datasets, y = Scores, fill = Assessment)) + 
  geom_boxplot() + 
  ylim(0, 27) +
  xlab("Dataset") +
  ylab("PHQ-9 Interval Means")#<<

#ggsave("Plots/k20_EMA-Datasets_Pre-Post_Boxplots_mit_EMA_5.5.jpg", width = 6, height = 4)#<<
#ggsave("Plots/k20_EMA-Datasets_Pre-Post_Boxplots.jpg", width = 6, height = 4)#<<

Prozentuale Überlappung der Pre-Mittelwerte

# Overlap-Plots zum Vergleich
final.plot(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_30.30_PRE_Mean = EMA_30.30$PRE_Mean), 
           overlap(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_30.30_PRE_Mean = EMA_30.30$PRE_Mean))$OV)

final.plot(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_Window_PRE_Mean = EMA_5.5_Window$PRE_Mean), 
           overlap(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_Window_PRE_Mean =
                          EMA_5.5_Window$PRE_Mean))$OV)

final.plot(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_Days_PRE_Mean = EMA_5.5_Days$PRE_Mean), 
           overlap(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_Days_PRE_Mean =
                          EMA_5.5_Days$PRE_Mean))$OV)

Prozentuale Überlappung der Post-Mittelwerte

# Overlap-Plots zum Vergleich
final.plot(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_30MZP_POST_Mean = EMA_30.30$POST_Mean), 
           overlap(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_30MZP_POST_Mean =
                          EMA_30.30$POST_Mean))$OV)

final.plot(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_Window_POST_Mean = EMA_5.5_Window$POST_Mean), 
           overlap(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_Window_POST_Mean =
                          EMA_5.5_Window$POST_Mean))$OV)

final.plot(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_Days_POST_Mean = EMA_5.5_Days$POST_Mean), 
           overlap(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_Days_POST_Mean = EMA_5.5_Days$POST_Mean))$OV)

---

1.3 Reliabilitäten und Inter-Item-Korrelationen

1.3.1 EMA_5.5 (je 5 MZP)

# Korrelationsmatrix von PRE- und POST-MZP:
EMA_5.5_KorMat = cor(EMA_5.5[, c(pre_5mzp, post_5mzp)]) %>% 
  round(., digits = 2)

# durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden MZP (beachte: ohne Fisher-Z-Transformation):
pre_inter_item_rtt = 0L
for (i in 1:4) {
  pre_inter_item_rtt = pre_inter_item_rtt + FisherZ(EMA_5.5_KorMat[i,i+1])
}
pre_inter_item_rtt = FisherZInv(pre_inter_item_rtt / 4)

post_inter_item_rtt = 0L
for (i in 5:9) {
  post_inter_item_rtt = post_inter_item_rtt + FisherZ(EMA_5.5_KorMat[i,i+1])
}
post_inter_item_rtt = FisherZInv(post_inter_item_rtt / 4)


for (i in 1:9) {
  EMA_5.5_KorMat[i, i+1] = cell_spec(EMA_5.5_KorMat[i, i+1], "html", bold = TRUE)
}

rownames(EMA_5.5_KorMat) = cell_spec(rownames(EMA_5.5_KorMat), "html", bold = TRUE)

EMA_5.5_KorMat %>%
  kable(., format = "html", escape = FALSE) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
                full_width = FALSE, fixed_thead = T)

	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5
PRE1_1	1	0.32	0.1	0.04	0.02	0.16	0.05	0.02	0.01	0.01
PRE1_2	0.32	1	0.32	0.12	0.05	0.05	0.01	0	0	0
PRE1_3	0.1	0.32	1	0.32	0.12	0	0	0.01	0.01	0
PRE1_4	0.04	0.12	0.32	1	0.32	0.01	0	0.02	0.01	0.02
PRE1_5	0.02	0.05	0.12	0.32	1	0	-0.01	0.01	0	0.02
POST1_1	0.16	0.05	0	0.01	0	1	0.32	0.1	0.04	0.01
POST1_2	0.05	0.01	0	0	-0.01	0.32	1	0.31	0.12	0.03
POST1_3	0.02	0	0.01	0.02	0.01	0.1	0.31	1	0.32	0.11
POST1_4	0.01	0	0.01	0.01	0	0.04	0.12	0.32	1	0.32
POST1_5	0.01	0	0	0.02	0.02	0.01	0.03	0.11	0.32	1

# mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP:
PRE_alpha = CronbachAlpha(EMA_5.5[pre_5mzp])
POST_alpha = CronbachAlpha(EMA_5.5[post_5mzp])
EMA_5.5_Alpha = FisherZInv(mean(c(FisherZ(PRE_alpha), FisherZ(POST_alpha))))

Korrelation zwischen den Pre- und Post-Intervall-Mittelwerten = 0.047.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Pre-MZP (Fisher-Z-transformiert): r = 0.32.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Post-MZP (Fisher-Z-transformiert): r = 0.32.
Mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP = 0.509.

---

1.3.2 EMA_30.30 (je 30 MZP)

# Korrelationsmatrix von PRE- und POST-MZP:
EMA_30.30_KorMat = cor(EMA_30.30[, c(pre_30mzp, post_30mzp)]) %>% 
  round(., digits = 2)

# durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden MZP (beachte: ohne Fisher-Z-Transformation):
pre_inter_item_rtt = 0L
for (i in 1:29) {
  pre_inter_item_rtt = pre_inter_item_rtt + FisherZ(EMA_30.30_KorMat[i,i+1])
}
pre_inter_item_rtt = FisherZInv(pre_inter_item_rtt / 29)

post_inter_item_rtt = 0L
for (i in 31:59) {
  post_inter_item_rtt = post_inter_item_rtt + FisherZ(EMA_30.30_KorMat[i,i+1])
}
post_inter_item_rtt = FisherZInv(post_inter_item_rtt / 29)


for (i in 1:59) {
  EMA_30.30_KorMat[i, i+1] = cell_spec(EMA_30.30_KorMat[i, i+1], "html", bold = TRUE)
}

rownames(EMA_30.30_KorMat) = cell_spec(rownames(EMA_30.30_KorMat), "html", bold = TRUE)

EMA_30.30_KorMat %>%
  kable(., format = "html", escape = FALSE) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
                full_width = FALSE, fixed_thead = T) %>%
  scroll_box(height = "800px")

	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	PRE1_6	PRE1_7	PRE1_8	PRE1_9	PRE1_10	PRE1_11	PRE1_12	PRE1_13	PRE1_14	PRE1_15	PRE1_16	PRE1_17	PRE1_18	PRE1_19	PRE1_20	PRE1_21	PRE1_22	PRE1_23	PRE1_24	PRE1_25	PRE1_26	PRE1_27	PRE1_28	PRE1_29	PRE1_30	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	POST1_6	POST1_7	POST1_8	POST1_9	POST1_10	POST1_11	POST1_12	POST1_13	POST1_14	POST1_15	POST1_16	POST1_17	POST1_18	POST1_19	POST1_20	POST1_21	POST1_22	POST1_23	POST1_24	POST1_25	POST1_26	POST1_27	POST1_28	POST1_29	POST1_30
PRE1_1	1	0.32	0.1	0.04	0.02	0.27	0.32	0.32	0.3	0.27	0.27	0.3	0.33	0.32	0.26	0.25	0.33	0.33	0.32	0.24	0.28	0.31	0.31	0.32	0.26	0.26	0.3	0.32	0.32	0.27	0.16	0.05	0.02	0.01	0.01	0.05	0.05	0.05	0.06	0.04	0.05	0.06	0.05	0.04	0.03	0.05	0.06	0.04	0.06	0.03	0.04	0.05	0.05	0.06	0.04	0.05	0.06	0.05	0.04	0.04
PRE1_2	0.32	1	0.32	0.12	0.05	0.33	0.38	0.39	0.38	0.33	0.33	0.39	0.39	0.39	0.31	0.33	0.4	0.42	0.39	0.29	0.33	0.4	0.39	0.38	0.32	0.33	0.38	0.39	0.37	0.33	0.05	0.01	0	0	0	0.03	0	0.01	0.01	0	0.02	0.01	0.01	0.01	0.01	0.01	0.02	0	0.02	0.02	0	0.01	0.01	0.01	0.02	0	0.02	0.03	0	0.01
PRE1_3	0.1	0.32	1	0.32	0.12	0.34	0.39	0.42	0.4	0.32	0.34	0.41	0.41	0.41	0.3	0.34	0.42	0.41	0.39	0.31	0.33	0.43	0.43	0.39	0.3	0.33	0.4	0.43	0.39	0.33	0	0	0.01	0.01	0	0.01	0.01	0.01	-0.01	0	0	0	0.02	0	0.01	0.01	0.01	-0.01	0	0.01	0	0.02	-0.01	0	0	0.02	0	0.01	0	0
PRE1_4	0.04	0.12	0.32	1	0.32	0.32	0.39	0.41	0.38	0.32	0.34	0.39	0.41	0.37	0.3	0.32	0.38	0.39	0.4	0.33	0.3	0.4	0.41	0.4	0.3	0.3	0.37	0.42	0.39	0.34	0.01	0	0.02	0.01	0.02	0	0.02	0.02	0.01	0.01	0	0.02	0.02	0	0.01	0.02	0.03	0	0	0	0.01	0.01	0.01	0	0.01	0	0.02	0.03	0	0
PRE1_5	0.02	0.05	0.12	0.32	1	0.27	0.33	0.34	0.33	0.25	0.28	0.33	0.33	0.32	0.26	0.27	0.31	0.31	0.33	0.3	0.26	0.35	0.32	0.32	0.26	0.28	0.33	0.34	0.31	0.26	0	-0.01	0.01	0	0.02	-0.01	0.02	0	0.01	0	0	0	0	0.02	0	0	0.01	0.01	0.01	0	0.01	0.01	0.02	0	-0.02	0.01	0.01	0.01	0	-0.01
PRE1_6	0.27	0.33	0.34	0.32	0.27	1	0.32	0.12	0.06	0.03	0.28	0.36	0.34	0.31	0.25	0.31	0.29	0.32	0.34	0.27	0.27	0.33	0.33	0.34	0.26	0.29	0.31	0.3	0.32	0.31	0.04	0.02	0	0	0.01	0	0.01	0.02	0.02	0.02	0.02	0.02	0.02	0.01	0.01	0.01	0.02	0.01	0.02	0.02	0.01	0.01	0.03	0.01	0.02	0.02	0.02	0.02	0.01	0
PRE1_7	0.32	0.38	0.39	0.39	0.33	0.32	1	0.33	0.1	0.06	0.33	0.38	0.39	0.41	0.3	0.37	0.39	0.36	0.39	0.3	0.32	0.4	0.42	0.41	0.28	0.3	0.4	0.42	0.38	0.31	0.04	0.01	0.01	0.02	0.01	0.03	0.03	0.02	0	0.01	0.02	0.02	0.03	0.01	0.02	0.02	0.03	0.01	0.01	0.01	0.02	0.01	0.01	0.01	0.03	0.01	0.02	0.03	0.01	0.01
PRE1_8	0.32	0.39	0.42	0.41	0.34	0.12	0.33	1	0.33	0.09	0.36	0.42	0.43	0.39	0.29	0.32	0.43	0.43	0.39	0.32	0.32	0.44	0.42	0.4	0.31	0.28	0.4	0.47	0.4	0.33	0.05	0.01	0.02	0	0	0.03	0.01	0.01	0.02	0.01	0.01	0	0.02	0.02	0.02	0.02	0.02	0.01	0.02	0.01	0.02	0.01	0.02	0.01	0.01	0.02	0.01	0.02	0.02	0.01
PRE1_9	0.3	0.38	0.4	0.38	0.33	0.06	0.1	0.33	1	0.32	0.33	0.36	0.4	0.39	0.31	0.29	0.39	0.39	0.38	0.34	0.31	0.4	0.39	0.37	0.33	0.33	0.39	0.39	0.39	0.3	0.06	0.01	0.03	0.01	0.01	0.02	0.02	0.03	0.03	0	0.02	0.03	0.03	0.02	0.01	0.03	0.03	0.02	0.02	0.02	0.02	0.03	0.02	0.03	0.01	0.02	0.02	0.04	0.01	0.03
PRE1_10	0.27	0.33	0.32	0.32	0.25	0.03	0.06	0.09	0.32	1	0.26	0.31	0.3	0.33	0.29	0.22	0.33	0.36	0.33	0.24	0.29	0.32	0.3	0.3	0.27	0.3	0.27	0.32	0.31	0.29	0.03	0	0.01	0.01	0.01	0	0.02	0.01	0.01	0.01	0	0.03	0.01	0.01	0	0.01	0.02	0	0.01	0.01	-0.01	0.03	0.01	0.02	0	0.01	0.02	0.02	-0.01	0
PRE1_11	0.27	0.33	0.34	0.34	0.28	0.28	0.33	0.36	0.33	0.26	1	0.37	0.13	0.07	0.01	0.3	0.33	0.34	0.35	0.24	0.29	0.35	0.35	0.34	0.24	0.28	0.34	0.31	0.36	0.27	0.04	0.01	0.02	0.01	0.03	0.03	0.02	0.03	0.01	0.01	0.02	0.03	0.03	0.02	0.01	0.02	0.02	0.01	0.02	0.03	0.02	0.03	0.01	0.03	0.02	0.01	0.02	0.04	0.02	0.01
PRE1_12	0.3	0.39	0.41	0.39	0.33	0.36	0.38	0.42	0.36	0.31	0.37	1	0.3	0.11	0.03	0.35	0.41	0.41	0.36	0.3	0.33	0.4	0.4	0.4	0.29	0.34	0.39	0.41	0.38	0.31	0.06	0.01	0	0.02	0	0.02	0.03	0.02	0	0.02	0.03	0.02	0.02	0	0.01	0.02	0.02	0	0.02	0.03	0.01	0.02	0.02	0.03	0.01	0.01	0.03	0.03	0	0.01
PRE1_13	0.33	0.39	0.41	0.41	0.33	0.34	0.39	0.43	0.4	0.3	0.13	0.3	1	0.33	0.1	0.3	0.41	0.41	0.41	0.34	0.33	0.4	0.38	0.41	0.33	0.34	0.37	0.43	0.41	0.32	0.03	0.01	0.01	0.01	0.01	0	0	0.02	0.03	0.01	0.03	0.01	0.01	0.01	0	0.03	0.03	0.01	0	0	0.01	0.02	0.02	0	0.01	0.02	0.02	0.01	0.01	0
PRE1_14	0.32	0.39	0.41	0.37	0.32	0.31	0.41	0.39	0.39	0.33	0.07	0.11	0.33	1	0.3	0.31	0.39	0.41	0.38	0.32	0.29	0.42	0.43	0.39	0.29	0.32	0.38	0.43	0.37	0.32	0.06	0.02	0	0	0.01	0.02	0.02	0.01	0.02	0.01	0.01	0.01	0.03	0.02	0.02	0.01	0.03	0.02	0.02	0	0.01	0.01	0.02	0.02	0.03	0.02	0.01	0.02	0.01	0.03
PRE1_15	0.26	0.31	0.3	0.3	0.26	0.25	0.3	0.29	0.31	0.29	0.01	0.03	0.1	0.3	1	0.25	0.29	0.29	0.34	0.27	0.26	0.32	0.3	0.27	0.29	0.22	0.29	0.32	0.27	0.33	0.03	0	0.03	-0.01	0	0.01	0.02	0.01	0.02	0	-0.01	0.02	0.02	0.02	0.01	0	0.02	0	0.02	0	0.01	0.02	0.02	0	0	0.01	0.01	0.03	0.01	0
PRE1_16	0.25	0.33	0.34	0.32	0.27	0.31	0.37	0.32	0.29	0.22	0.3	0.35	0.3	0.31	0.25	1	0.31	0.11	0.07	0.03	0.24	0.32	0.34	0.34	0.27	0.26	0.31	0.35	0.29	0.3	0.03	0	0	0.01	0	0	0.01	0.01	0.01	0.01	0.02	0.02	0.02	0.01	-0.01	0	0.01	0.01	0.02	0.01	0.01	0.01	0	0.03	0.01	0.01	0.02	0.02	0	0
PRE1_17	0.33	0.4	0.42	0.38	0.31	0.29	0.39	0.43	0.39	0.33	0.33	0.41	0.41	0.39	0.29	0.31	1	0.36	0.13	0.04	0.3	0.4	0.44	0.37	0.32	0.34	0.38	0.42	0.41	0.28	0.07	0.01	0.01	0.02	0	0.02	0.03	0.02	0.01	0.02	0.01	0.03	0.03	0.03	0.01	0.03	0.03	0.01	0.01	0.03	0.01	0.01	0.04	0.02	0.02	0.02	0.02	0.04	0.01	0.01
PRE1_18	0.33	0.42	0.41	0.39	0.31	0.32	0.36	0.43	0.39	0.36	0.34	0.41	0.41	0.41	0.29	0.11	0.36	1	0.31	0.08	0.35	0.41	0.4	0.41	0.29	0.36	0.39	0.38	0.38	0.35	0.06	0.03	0.01	-0.01	0	0.03	0.03	0.01	0.02	0.01	0.01	0.02	0.03	0.02	0.01	0.02	0.02	0.01	0.02	0.02	0.01	0.03	0.01	0.02	0.01	0.01	0.01	0.04	0.01	0.01
PRE1_19	0.32	0.39	0.39	0.4	0.33	0.34	0.39	0.39	0.38	0.33	0.35	0.36	0.41	0.38	0.34	0.07	0.13	0.31	1	0.33	0.35	0.43	0.39	0.37	0.3	0.3	0.38	0.42	0.4	0.35	0.03	0	0.02	0.01	0.03	0.03	0.01	0.03	0.01	0	0.01	0.01	0.02	0.02	0.03	0.02	0.03	0.01	0.03	0.01	0.01	0.03	0.02	0.01	0.02	0.02	0.03	0.03	0.01	0.01
PRE1_20	0.24	0.29	0.31	0.33	0.3	0.27	0.3	0.32	0.34	0.24	0.24	0.3	0.34	0.32	0.27	0.03	0.04	0.08	0.33	1	0.27	0.33	0.29	0.33	0.25	0.24	0.32	0.34	0.31	0.27	0.02	0.01	0.03	0	0.01	0	0.01	0.03	0.02	0	0.02	0.01	0.01	0.01	0.02	0.02	0.03	0	0.01	0	0.02	0.02	0.02	-0.01	0.01	0.02	0.01	0.01	0.01	0.01
PRE1_21	0.28	0.33	0.33	0.3	0.26	0.27	0.32	0.32	0.31	0.29	0.29	0.33	0.33	0.29	0.26	0.24	0.3	0.35	0.35	0.27	1	0.33	0.1	0.07	0.01	0.27	0.33	0.3	0.34	0.27	0.04	0.02	0.01	0.01	0	0.01	0.01	0.01	0.03	0.01	0.03	0.02	0.01	0.01	0.01	0.02	0.01	0.01	0.01	0.03	0.01	0.03	0.03	0.01	0	0.02	0.02	0.01	0.01	0.01
PRE1_22	0.31	0.4	0.43	0.4	0.35	0.33	0.4	0.44	0.4	0.32	0.35	0.4	0.4	0.42	0.32	0.32	0.4	0.41	0.43	0.33	0.33	1	0.37	0.15	0.05	0.34	0.39	0.43	0.39	0.34	0.04	0.01	0.01	-0.02	0	0.02	0.02	0.02	0	-0.01	0	0	0.01	0.01	0.02	0	0.03	-0.01	0.01	0.02	0.02	0.01	0.01	0.01	-0.01	0.01	-0.01	0.04	0	0.01
PRE1_23	0.31	0.39	0.43	0.41	0.32	0.33	0.42	0.42	0.39	0.3	0.35	0.4	0.38	0.43	0.3	0.34	0.44	0.4	0.39	0.29	0.1	0.37	1	0.31	0.08	0.31	0.36	0.43	0.43	0.33	0.05	0.01	0.01	0	0.01	0.03	0.01	0.02	0.02	0.01	0.02	0.02	0.02	0.02	0.01	0.02	0.04	0.02	0.01	0	0.01	0.02	0	0.03	0.02	0.01	0.02	0.03	0.01	0
PRE1_24	0.32	0.38	0.39	0.4	0.32	0.34	0.41	0.4	0.37	0.3	0.34	0.4	0.41	0.39	0.27	0.34	0.37	0.41	0.37	0.33	0.07	0.15	0.31	1	0.29	0.31	0.36	0.45	0.35	0.34	0.04	0.01	0.01	0.02	0.01	0.01	0.02	0.02	0.02	0.02	0.01	0.03	0.04	0.02	-0.01	0.03	0.03	0.02	0.01	0	0.01	0.02	0.01	0.02	0.03	0	0.03	0.03	0.02	0.01
PRE1_25	0.26	0.32	0.3	0.3	0.26	0.26	0.28	0.31	0.33	0.27	0.24	0.29	0.33	0.29	0.29	0.27	0.32	0.29	0.3	0.25	0.01	0.05	0.08	0.29	1	0.27	0.32	0.31	0.27	0.27	0.03	-0.01	0.03	0.02	0.02	0.01	0.03	0.03	0.02	0.01	0.01	0.03	0.03	0.01	0.02	0.01	0.02	0.01	0.04	0.02	0	0.02	0.03	0.01	0.03	0.03	0.03	0.02	0	0.02
PRE1_26	0.26	0.33	0.33	0.3	0.28	0.29	0.3	0.28	0.33	0.3	0.28	0.34	0.34	0.32	0.22	0.26	0.34	0.36	0.3	0.24	0.27	0.34	0.31	0.31	0.27	1	0.29	0.12	0.05	0.03	0.03	0.02	0.01	0	-0.02	0	0.01	0.02	0.01	0	0.01	0.02	0.01	0	0	0	0.02	0	0.01	0.02	0	0.02	0	0	0.01	0	0	0.03	0.01	0
PRE1_27	0.3	0.38	0.4	0.37	0.33	0.31	0.4	0.4	0.39	0.27	0.34	0.39	0.37	0.38	0.29	0.31	0.38	0.39	0.38	0.32	0.33	0.39	0.36	0.36	0.32	0.29	1	0.36	0.09	0.05	0.05	0	0.01	-0.02	0.02	0.02	0.02	0.02	0.01	0	0.01	0.02	0.01	0	0.02	0.01	0.02	0.01	0.02	0.01	0	0.02	0.02	0.02	0.01	0.01	0.02	0.03	0.01	0
PRE1_28	0.32	0.39	0.43	0.42	0.34	0.3	0.42	0.47	0.39	0.32	0.31	0.41	0.43	0.43	0.32	0.35	0.42	0.38	0.42	0.34	0.3	0.43	0.43	0.45	0.31	0.12	0.36	1	0.31	0.12	0.05	0	0	0	0.01	0.02	0.03	0.01	0.01	0.01	0	0.01	0.02	0.02	0.02	0.03	0.01	0	0.01	0.01	0.02	0	0.01	0.02	0.02	0.01	0.02	0.03	0	0.01
PRE1_29	0.32	0.37	0.39	0.39	0.31	0.32	0.38	0.4	0.39	0.31	0.36	0.38	0.41	0.37	0.27	0.29	0.41	0.38	0.4	0.31	0.34	0.39	0.43	0.35	0.27	0.05	0.09	0.31	1	0.35	0.06	0.02	0.01	0.02	0.02	0.04	0.02	0.03	0.03	0.02	0.03	0.03	0.04	0.03	0.01	0.04	0.04	0.01	0.02	0.02	0.02	0.03	0.02	0.02	0.03	0.03	0.04	0.02	0.01	0.03
PRE1_30	0.27	0.33	0.33	0.34	0.26	0.31	0.31	0.33	0.3	0.29	0.27	0.31	0.32	0.32	0.33	0.3	0.28	0.35	0.35	0.27	0.27	0.34	0.33	0.34	0.27	0.03	0.05	0.12	0.35	1	0.03	0.01	0.02	0.02	0	0.01	0.02	0.02	0.03	0.02	0.02	0.01	0.04	0.02	0.01	0.01	0.03	0.02	0.03	0.01	0.02	0.03	0.03	0.01	0	0.02	0.02	0.03	0.01	0.01
POST1_1	0.16	0.05	0	0.01	0	0.04	0.04	0.05	0.06	0.03	0.04	0.06	0.03	0.06	0.03	0.03	0.07	0.06	0.03	0.02	0.04	0.04	0.05	0.04	0.03	0.03	0.05	0.05	0.06	0.03	1	0.32	0.1	0.04	0.01	0.28	0.34	0.31	0.3	0.25	0.26	0.32	0.31	0.32	0.26	0.27	0.31	0.31	0.31	0.27	0.27	0.31	0.31	0.31	0.27	0.26	0.3	0.32	0.31	0.28
POST1_2	0.05	0.01	0	0	-0.01	0.02	0.01	0.01	0.01	0	0.01	0.01	0.01	0.02	0	0	0.01	0.03	0	0.01	0.02	0.01	0.01	0.01	-0.01	0.02	0	0	0.02	0.01	0.32	1	0.31	0.12	0.03	0.32	0.39	0.4	0.38	0.29	0.31	0.38	0.38	0.39	0.32	0.31	0.39	0.38	0.38	0.32	0.32	0.37	0.38	0.39	0.32	0.29	0.36	0.43	0.38	0.32
POST1_3	0.02	0	0.01	0.02	0.01	0	0.01	0.02	0.03	0.01	0.02	0	0.01	0	0.03	0	0.01	0.01	0.02	0.03	0.01	0.01	0.01	0.01	0.03	0.01	0.01	0	0.01	0.02	0.1	0.31	1	0.32	0.11	0.3	0.38	0.42	0.4	0.33	0.3	0.39	0.43	0.4	0.31	0.32	0.4	0.4	0.38	0.33	0.33	0.4	0.4	0.38	0.32	0.31	0.38	0.42	0.39	0.33
POST1_4	0.01	0	0.01	0.01	0	0	0.02	0	0.01	0.01	0.01	0.02	0.01	0	-0.01	0.01	0.02	-0.01	0.01	0	0.01	-0.02	0	0.02	0.02	0	-0.02	0	0.02	0.02	0.04	0.12	0.32	1	0.32	0.33	0.38	0.39	0.39	0.31	0.31	0.38	0.41	0.39	0.32	0.32	0.4	0.4	0.37	0.31	0.31	0.38	0.42	0.37	0.32	0.3	0.38	0.4	0.4	0.32
POST1_5	0.01	0	0	0.02	0.02	0.01	0.01	0	0.01	0.01	0.03	0	0.01	0.01	0	0	0	0	0.03	0.01	0	0	0.01	0.01	0.02	-0.02	0.02	0.01	0.02	0	0.01	0.03	0.11	0.32	1	0.25	0.31	0.32	0.34	0.27	0.27	0.31	0.33	0.31	0.27	0.26	0.31	0.33	0.32	0.27	0.27	0.33	0.34	0.3	0.24	0.25	0.31	0.33	0.31	0.28
POST1_6	0.05	0.03	0.01	0	-0.01	0	0.03	0.03	0.02	0	0.03	0.02	0	0.02	0.01	0	0.02	0.03	0.03	0	0.01	0.02	0.03	0.01	0.01	0	0.02	0.02	0.04	0.01	0.28	0.32	0.3	0.33	0.25	1	0.34	0.12	0.04	-0.01	0.26	0.33	0.31	0.3	0.27	0.26	0.33	0.32	0.31	0.27	0.27	0.34	0.34	0.26	0.27	0.26	0.27	0.33	0.35	0.27
POST1_7	0.05	0	0.01	0.02	0.02	0.01	0.03	0.01	0.02	0.02	0.02	0.03	0	0.02	0.02	0.01	0.03	0.03	0.01	0.01	0.01	0.02	0.01	0.02	0.03	0.01	0.02	0.03	0.02	0.02	0.34	0.39	0.38	0.38	0.31	0.34	1	0.31	0.12	0.04	0.31	0.37	0.37	0.4	0.34	0.3	0.38	0.39	0.4	0.33	0.33	0.37	0.39	0.38	0.33	0.29	0.38	0.42	0.38	0.32
POST1_8	0.05	0.01	0.01	0.02	0	0.02	0.02	0.01	0.03	0.01	0.03	0.02	0.02	0.01	0.01	0.01	0.02	0.01	0.03	0.03	0.01	0.02	0.02	0.02	0.03	0.02	0.02	0.01	0.03	0.02	0.31	0.4	0.42	0.39	0.32	0.12	0.31	1	0.32	0.09	0.3	0.38	0.42	0.42	0.31	0.29	0.4	0.41	0.4	0.34	0.33	0.38	0.39	0.4	0.33	0.29	0.39	0.41	0.39	0.35
POST1_9	0.06	0.01	-0.01	0.01	0.01	0.02	0	0.02	0.03	0.01	0.01	0	0.03	0.02	0.02	0.01	0.01	0.02	0.01	0.02	0.03	0	0.02	0.02	0.02	0.01	0.01	0.01	0.03	0.03	0.3	0.38	0.4	0.39	0.34	0.04	0.12	0.32	1	0.33	0.31	0.39	0.41	0.38	0.32	0.33	0.4	0.39	0.38	0.31	0.32	0.37	0.41	0.4	0.31	0.32	0.39	0.42	0.37	0.32
POST1_10	0.04	0	0	0.01	0	0.02	0.01	0.01	0	0.01	0.01	0.02	0.01	0.01	0	0.01	0.02	0.01	0	0	0.01	-0.01	0.01	0.02	0.01	0	0	0.01	0.02	0.02	0.25	0.29	0.33	0.31	0.27	-0.01	0.04	0.09	0.33	1	0.26	0.3	0.34	0.31	0.24	0.29	0.31	0.3	0.28	0.26	0.25	0.33	0.33	0.31	0.23	0.25	0.3	0.32	0.29	0.28
POST1_11	0.05	0.02	0	0	0	0.02	0.02	0.01	0.02	0	0.02	0.03	0.03	0.01	-0.01	0.02	0.01	0.01	0.01	0.02	0.03	0	0.02	0.01	0.01	0.01	0.01	0	0.03	0.02	0.26	0.31	0.3	0.31	0.27	0.26	0.31	0.3	0.31	0.26	1	0.29	0.1	0.06	0.01	0.29	0.35	0.29	0.27	0.25	0.28	0.3	0.32	0.3	0.26	0.24	0.26	0.34	0.33	0.28
POST1_12	0.06	0.01	0	0.02	0	0.02	0.02	0	0.03	0.03	0.03	0.02	0.01	0.01	0.02	0.02	0.03	0.02	0.01	0.01	0.02	0	0.02	0.03	0.03	0.02	0.02	0.01	0.03	0.01	0.32	0.38	0.39	0.38	0.31	0.33	0.37	0.38	0.39	0.3	0.29	1	0.32	0.12	0.05	0.32	0.38	0.38	0.38	0.31	0.3	0.36	0.37	0.41	0.33	0.3	0.35	0.41	0.38	0.33
POST1_13	0.05	0.01	0.02	0.02	0	0.02	0.03	0.02	0.03	0.01	0.03	0.02	0.01	0.03	0.02	0.02	0.03	0.03	0.02	0.01	0.01	0.01	0.02	0.04	0.03	0.01	0.01	0.02	0.04	0.04	0.31	0.38	0.43	0.41	0.33	0.31	0.37	0.42	0.41	0.34	0.1	0.32	1	0.33	0.12	0.31	0.38	0.42	0.43	0.33	0.3	0.4	0.45	0.38	0.32	0.31	0.4	0.42	0.38	0.35
POST1_14	0.04	0.01	0	0	0.02	0.01	0.01	0.02	0.02	0.01	0.02	0	0.01	0.02	0.02	0.01	0.03	0.02	0.02	0.01	0.01	0.01	0.02	0.02	0.01	0	0	0.02	0.03	0.02	0.32	0.39	0.4	0.39	0.31	0.3	0.4	0.42	0.38	0.31	0.06	0.12	0.33	1	0.28	0.31	0.37	0.4	0.38	0.34	0.32	0.38	0.4	0.38	0.32	0.31	0.41	0.41	0.36	0.31
POST1_15	0.03	0.01	0.01	0.01	0	0.01	0.02	0.02	0.01	0	0.01	0.01	0	0.02	0.01	-0.01	0.01	0.01	0.03	0.02	0.01	0.02	0.01	-0.01	0.02	0	0.02	0.02	0.01	0.01	0.26	0.32	0.31	0.32	0.27	0.27	0.34	0.31	0.32	0.24	0.01	0.05	0.12	0.28	1	0.25	0.33	0.33	0.3	0.27	0.3	0.34	0.31	0.28	0.24	0.24	0.31	0.33	0.33	0.27
POST1_16	0.05	0.01	0.01	0.02	0	0.01	0.02	0.02	0.03	0.01	0.02	0.02	0.03	0.01	0	0	0.03	0.02	0.02	0.02	0.02	0	0.02	0.03	0.01	0	0.01	0.03	0.04	0.01	0.27	0.31	0.32	0.32	0.26	0.26	0.3	0.29	0.33	0.29	0.29	0.32	0.31	0.31	0.25	1	0.32	0.09	0.03	0.02	0.24	0.32	0.32	0.33	0.27	0.28	0.3	0.34	0.3	0.25
POST1_17	0.06	0.02	0.01	0.03	0.01	0.02	0.03	0.02	0.03	0.02	0.02	0.02	0.03	0.03	0.02	0.01	0.03	0.02	0.03	0.03	0.01	0.03	0.04	0.03	0.02	0.02	0.02	0.01	0.04	0.03	0.31	0.39	0.4	0.4	0.31	0.33	0.38	0.4	0.4	0.31	0.35	0.38	0.38	0.37	0.33	0.32	1	0.32	0.11	0.07	0.32	0.41	0.39	0.36	0.32	0.31	0.36	0.42	0.4	0.33
POST1_18	0.04	0	-0.01	0	0.01	0.01	0.01	0.01	0.02	0	0.01	0	0.01	0.02	0	0.01	0.01	0.01	0.01	0	0.01	-0.01	0.02	0.02	0.01	0	0.01	0	0.01	0.02	0.31	0.38	0.4	0.4	0.33	0.32	0.39	0.41	0.39	0.3	0.29	0.38	0.42	0.4	0.33	0.09	0.32	1	0.3	0.1	0.3	0.39	0.41	0.38	0.33	0.28	0.39	0.42	0.42	0.32
POST1_19	0.06	0.02	0	0	0.01	0.02	0.01	0.02	0.02	0.01	0.02	0.02	0	0.02	0.02	0.02	0.01	0.02	0.03	0.01	0.01	0.01	0.01	0.01	0.04	0.01	0.02	0.01	0.02	0.03	0.31	0.38	0.38	0.37	0.32	0.31	0.4	0.4	0.38	0.28	0.27	0.38	0.43	0.38	0.3	0.03	0.11	0.3	1	0.33	0.32	0.35	0.4	0.39	0.3	0.29	0.38	0.38	0.36	0.35
POST1_20	0.03	0.02	0.01	0	0	0.02	0.01	0.01	0.02	0.01	0.03	0.03	0	0	0	0.01	0.03	0.02	0.01	0	0.03	0.02	0	0	0.02	0.02	0.01	0.01	0.02	0.01	0.27	0.32	0.33	0.31	0.27	0.27	0.33	0.34	0.31	0.26	0.25	0.31	0.33	0.34	0.27	0.02	0.07	0.1	0.33	1	0.31	0.32	0.33	0.29	0.25	0.25	0.3	0.36	0.3	0.29
POST1_21	0.04	0	0	0.01	0.01	0.01	0.02	0.02	0.02	-0.01	0.02	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.02	0.01	0.02	0.01	0.01	0	0	0	0.02	0.02	0.02	0.27	0.32	0.33	0.31	0.27	0.27	0.33	0.33	0.32	0.25	0.28	0.3	0.3	0.32	0.3	0.24	0.32	0.3	0.32	0.31	1	0.33	0.14	0.02	0.02	0.25	0.29	0.32	0.34	0.31
POST1_22	0.05	0.01	0.02	0.01	0.01	0.01	0.01	0.01	0.03	0.03	0.03	0.02	0.02	0.01	0.02	0.01	0.01	0.03	0.03	0.02	0.03	0.01	0.02	0.02	0.02	0.02	0.02	0	0.03	0.03	0.31	0.37	0.4	0.38	0.33	0.34	0.37	0.38	0.37	0.33	0.3	0.36	0.4	0.38	0.34	0.32	0.41	0.39	0.35	0.32	0.33	1	0.32	0.11	0.04	0.3	0.34	0.42	0.41	0.32
POST1_23	0.05	0.01	-0.01	0.01	0.02	0.03	0.01	0.02	0.02	0.01	0.01	0.02	0.02	0.02	0.02	0	0.04	0.01	0.02	0.02	0.03	0.01	0	0.01	0.03	0	0.02	0.01	0.02	0.03	0.31	0.38	0.4	0.42	0.34	0.34	0.39	0.39	0.41	0.33	0.32	0.37	0.45	0.4	0.31	0.32	0.39	0.41	0.4	0.33	0.14	0.32	1	0.29	0.09	0.31	0.36	0.44	0.39	0.35
POST1_24	0.06	0.01	0	0	0	0.01	0.01	0.01	0.03	0.02	0.03	0.03	0	0.02	0	0.03	0.02	0.02	0.01	-0.01	0.01	0.01	0.03	0.02	0.01	0	0.02	0.02	0.02	0.01	0.31	0.39	0.38	0.37	0.3	0.26	0.38	0.4	0.4	0.31	0.3	0.41	0.38	0.38	0.28	0.33	0.36	0.38	0.39	0.29	0.02	0.11	0.29	1	0.32	0.31	0.4	0.4	0.33	0.3
POST1_25	0.04	0.02	0	0.01	-0.02	0.02	0.03	0.01	0.01	0	0.02	0.01	0.01	0.03	0	0.01	0.02	0.01	0.02	0.01	0	-0.01	0.02	0.03	0.03	0.01	0.01	0.02	0.03	0	0.27	0.32	0.32	0.32	0.24	0.27	0.33	0.33	0.31	0.23	0.26	0.33	0.32	0.32	0.24	0.27	0.32	0.33	0.3	0.25	0.02	0.04	0.09	0.32	1	0.24	0.33	0.33	0.31	0.26
POST1_26	0.05	0	0.02	0	0.01	0.02	0.01	0.02	0.02	0.01	0.01	0.01	0.02	0.02	0.01	0.01	0.02	0.01	0.02	0.02	0.02	0.01	0.01	0	0.03	0	0.01	0.01	0.03	0.02	0.26	0.29	0.31	0.3	0.25	0.26	0.29	0.29	0.32	0.25	0.24	0.3	0.31	0.31	0.24	0.28	0.31	0.28	0.29	0.25	0.25	0.3	0.31	0.31	0.24	1	0.27	0.12	0.03	0.01
POST1_27	0.06	0.02	0	0.02	0.01	0.02	0.02	0.01	0.02	0.02	0.02	0.03	0.02	0.01	0.01	0.02	0.02	0.01	0.03	0.01	0.02	-0.01	0.02	0.03	0.03	0	0.02	0.02	0.04	0.02	0.3	0.36	0.38	0.38	0.31	0.27	0.38	0.39	0.39	0.3	0.26	0.35	0.4	0.41	0.31	0.3	0.36	0.39	0.38	0.3	0.29	0.34	0.36	0.4	0.33	0.27	1	0.31	0.11	0.03
POST1_28	0.05	0.03	0.01	0.03	0.01	0.02	0.03	0.02	0.04	0.02	0.04	0.03	0.01	0.02	0.03	0.02	0.04	0.04	0.03	0.01	0.01	0.04	0.03	0.03	0.02	0.03	0.03	0.03	0.02	0.03	0.32	0.43	0.42	0.4	0.33	0.33	0.42	0.41	0.42	0.32	0.34	0.41	0.42	0.41	0.33	0.34	0.42	0.42	0.38	0.36	0.32	0.42	0.44	0.4	0.33	0.12	0.31	1	0.33	0.15
POST1_29	0.04	0	0	0	0	0.01	0.01	0.02	0.01	-0.01	0.02	0	0.01	0.01	0.01	0	0.01	0.01	0.01	0.01	0.01	0	0.01	0.02	0	0.01	0.01	0	0.01	0.01	0.31	0.38	0.39	0.4	0.31	0.35	0.38	0.39	0.37	0.29	0.33	0.38	0.38	0.36	0.33	0.3	0.4	0.42	0.36	0.3	0.34	0.41	0.39	0.33	0.31	0.03	0.11	0.33	1	0.32
POST1_30	0.04	0.01	0	0	-0.01	0	0.01	0.01	0.03	0	0.01	0.01	0	0.03	0	0	0.01	0.01	0.01	0.01	0.01	0.01	0	0.01	0.02	0	0	0.01	0.03	0.01	0.28	0.32	0.33	0.32	0.28	0.27	0.32	0.35	0.32	0.28	0.28	0.33	0.35	0.31	0.27	0.25	0.33	0.32	0.35	0.29	0.31	0.32	0.35	0.3	0.26	0.01	0.03	0.15	0.32	1

# mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP:
PRE_alpha = CronbachAlpha(EMA_30.30[pre_30mzp])
POST_alpha = CronbachAlpha(EMA_30.30[post_30mzp])
EMA_30.30_Alpha = FisherZInv(mean(c(FisherZ(PRE_alpha), FisherZ(POST_alpha))))

Korrelation zwischen den Pre- und Post-Intervall-Mittelwerten = 0.047.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Pre-MZP (Fisher-Z-transformiert): r = 0.31.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Post-MZP (Fisher-Z-transformiert): r = 0.31.
Mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP = 0.932.

---

1.3.3 EMA_5.5_Window (je 5 MZP)

# Korrelationsmatrix von PRE- und POST-MZP:
EMA_5.5_Window_KorMat = cor(EMA_5.5_Window[, c(pre_5mzp, post_5mzp)]) %>% 
  round(., digits = 2)

# durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden MZP (beachte: ohne Fisher-Z-Transformation):
pre_inter_item_rtt = 0L
for (i in 1:4) {
  pre_inter_item_rtt = pre_inter_item_rtt + FisherZ(EMA_5.5_Window_KorMat[i,i+1])
}
pre_inter_item_rtt = FisherZInv(pre_inter_item_rtt / 4)

post_inter_item_rtt = 0L
for (i in 5:9) {
  post_inter_item_rtt = post_inter_item_rtt + FisherZ(EMA_5.5_Window_KorMat[i,i+1])
}
post_inter_item_rtt = FisherZInv(post_inter_item_rtt / 4)


for (i in 1:9) {
  EMA_5.5_Window_KorMat[i, i+1] = cell_spec(EMA_5.5_Window_KorMat[i, i+1], "html", bold = TRUE)
}

rownames(EMA_5.5_Window_KorMat) = cell_spec(rownames(EMA_5.5_Window_KorMat), "html", bold = TRUE)

EMA_5.5_Window_KorMat %>%
  kable(., format = "html", escape = FALSE) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
                full_width = FALSE, fixed_thead = T)

	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5
PRE1_1	1	0.32	0.18	0.24	0.3	0.02	0	0.02	0.03	0.01
PRE1_2	0.32	1	0.3	0.19	0.22	0.03	0.02	0.01	0.02	0.02
PRE1_3	0.18	0.3	1	0.31	0.17	0.02	0.02	0.02	0.02	0.02
PRE1_4	0.24	0.19	0.31	1	0.31	0.01	0.03	0.03	0.01	0.02
PRE1_5	0.3	0.22	0.17	0.31	1	0.03	0.01	0.02	0.01	0.02
POST1_1	0.02	0.03	0.02	0.01	0.03	1	0.3	0.19	0.21	0.26
POST1_2	0	0.02	0.02	0.03	0.01	0.3	1	0.3	0.19	0.19
POST1_3	0.02	0.01	0.02	0.03	0.02	0.19	0.3	1	0.31	0.17
POST1_4	0.03	0.02	0.02	0.01	0.01	0.21	0.19	0.31	1	0.32
POST1_5	0.01	0.02	0.02	0.02	0.02	0.26	0.19	0.17	0.32	1

# mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP:
PRE_alpha = CronbachAlpha(EMA_5.5_Window[pre_5mzp])
POST_alpha = CronbachAlpha(EMA_5.5_Window[post_5mzp])
EMA_5.5_Window_Alpha = FisherZInv(mean(c(FisherZ(PRE_alpha), FisherZ(POST_alpha))))

Korrelation zwischen den Pre- und Post-Intervall-Mittelwerten = 0.045.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Pre-MZP (Fisher-Z-transformiert): r = 0.31.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Post-MZP (Fisher-Z-transformiert): r = 0.31.
Mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP = 0.623.

---

1.3.4 EMA_5.5_Days (je 5 MZP)

# Korrelationsmatrix von PRE- und POST-MZP:
EMA_5.5_Days_KorMat = cor(EMA_5.5_Days[, c(pre_5mzp, post_5mzp)]) %>% 
  round(., digits = 2)

# durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden MZP (beachte: ohne Fisher-Z-Transformation):
pre_inter_item_rtt = 0L
for (i in 1:4) {
  pre_inter_item_rtt = pre_inter_item_rtt + FisherZ(EMA_5.5_Days_KorMat[i,i+1])
}
pre_inter_item_rtt = FisherZInv(pre_inter_item_rtt / 4)

post_inter_item_rtt = 0L
for (i in 5:9) {
  post_inter_item_rtt = post_inter_item_rtt + FisherZ(EMA_5.5_Days_KorMat[i,i+1])
}
post_inter_item_rtt = FisherZInv(post_inter_item_rtt / 4)


for (i in 1:9) {
  EMA_5.5_Days_KorMat[i, i+1] = cell_spec(EMA_5.5_Days_KorMat[i, i+1], "html", bold = TRUE)
}

rownames(EMA_5.5_Days_KorMat) = cell_spec(rownames(EMA_5.5_Days_KorMat), "html", bold = TRUE)

EMA_5.5_Days_KorMat %>%
  kable(., format = "html", escape = FALSE) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
                full_width = FALSE, fixed_thead = T)

	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5
PRE1_1	1	0.28	0.34	0.36	0.33	0	0.02	0.01	0	0.02
PRE1_2	0.28	1	0.3	0.35	0.35	0	0.02	0.01	0	0.02
PRE1_3	0.34	0.3	1	0.31	0.36	0	0.02	0.01	0.01	0.02
PRE1_4	0.36	0.35	0.31	1	0.28	-0.01	0.01	0	-0.02	-0.01
PRE1_5	0.33	0.35	0.36	0.28	1	0.01	0.01	0.02	0.02	0.01
POST1_1	0	0	0	-0.01	0.01	1	0.28	0.34	0.35	0.33
POST1_2	0.02	0.02	0.02	0.01	0.01	0.28	1	0.3	0.34	0.32
POST1_3	0.01	0.01	0.01	0	0.02	0.34	0.3	1	0.31	0.32
POST1_4	0	0	0.01	-0.02	0.02	0.35	0.34	0.31	1	0.29
POST1_5	0.02	0.02	0.02	-0.01	0.01	0.33	0.32	0.32	0.29	1

# mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP:
PRE_alpha = CronbachAlpha(EMA_5.5_Days[pre_5mzp])
POST_alpha = CronbachAlpha(EMA_5.5_Days[post_5mzp])
EMA_5.5_Days_Alpha = FisherZInv(mean(c(FisherZ(PRE_alpha), FisherZ(POST_alpha))))

Korrelation zwischen den Pre- und Post-Intervall-Mittelwerten = 0.016.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Pre-MZP (Fisher-Z-transformiert): r = 0.29.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Post-MZP (Fisher-Z-transformiert): r = 0.3.
Mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP = 0.703.

---

1.4 Pre-Post-Differenz

Verteilungen der Pre-Post-Mittelwerts-Veränderungen

temp = tibble(MeanDiffs = c(EMA_5.5$MeanDiff, EMA_30.30$MeanDiff, EMA_5.5_Window$MeanDiff, EMA_5.5_Days$MeanDiff),
              Datasets = rep(as_factor(c("EMA_5.5", "EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days")), each = length(EMA_5.5$MeanDiff)))#<<

temp %>%
  ggplot(aes(x = MeanDiffs, fill = Datasets)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(x = "PHQ-9 Pre-Post Difference", y = "")#<<

#ggsave("Plots/k20_PP-Datasets_Pre-Post-Diff_Histogram.jpg", width = 6, height = 4)#<<

scatter.hist(EMA_5.5$MeanDiff, EMA_30.30$MeanDiff, xlab = "EMA_5.5$MeanDiff",
  ylab = "EMA_30.30$MeanDiff", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

scatter.hist(EMA_5.5$MeanDiff, EMA_5.5_Window$MeanDiff, xlab = "EMA_5.5$MeanDiff",
  ylab = "EMA_5.5_Window$MeanDiff", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

scatter.hist(EMA_5.5$MeanDiff, EMA_5.5_Days$MeanDiff, xlab = "EMA_5.5$MeanDiff",
  ylab = "EMA_5.5_Days$MeanDiff", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

scatter.hist(EMA_5.5_Window$MeanDiff, EMA_5.5_Days$MeanDiff, xlab = "EMA_5.5_Window$MeanDiff",
  ylab = "EMA_5.5_Days$MeanDiff", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Korrelation zwischen den Pre-Post-Differenzen in EMA_5.5 und EMA_30.30 = 1.
Korrelation zwischen den Pre-Post-Differenzen in EMA_5.5_Window und EMA_30.30 = 0.913.
Korrelation zwischen den Pre-Post-Differenzen in EMA_5.5_Days und EMA_30.30 = 0.859.

Prozentuale Überlappung der Pre-Post-Mittelwerts-Veränderungen

# Overlap-Plots zum Vergleich
final.plot(list(EMA_5.5_MeanDiff = EMA_5.5$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff), 
           overlap(list(EMA_5.5_MeanDiff = EMA_5.5$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff))$OV)

final.plot(list(EMA_5.5_Window_MeanDiff = EMA_5.5_Window$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff), 
           overlap(list(EMA_5.5_Window_MeanDiff = EMA_5.5_Window$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff))$OV)

final.plot(list(EMA_5.5_Days_MeanDiff = EMA_5.5_Days$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff), 
           overlap(list(EMA_5.5_Days_MeanDiff = EMA_5.5_Days$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff))$OV)

final.plot(list(EMA_5.5_Window_MeanDiff = EMA_5.5_Window$MeanDiff, EMA_5.5_Days_MeanDiff = EMA_5.5_Days$MeanDiff), 
           overlap(list(EMA_5.5_Window_MeanDiff = EMA_5.5_Window$MeanDiff, EMA_5.5_Days_MeanDiff = EMA_5.5_Days$MeanDiff))$OV)

---

1.4.1 Cohen´s d

Cohen´s d (mit gepoolten SDs) vom Pre- zum Post-Intervall in EMA_5.5 (je 5 MZP)

\[ d = \frac{\overline{x_{1}} - \overline{x_{2}}} {\sqrt{0.5 \cdot (s_{x}^2 + s_{y}^2)}} \]

\(\overline{x_{1}}\) = mean of subject´s pretest scores, \(\overline{x_{2}}\) = mean of subject´s posttest scores, \(s_{x}\) = individual standard deviation of pretest time points, \(s_{y}\) = individual standard deviation of posttest time points

EMA_5.5$Cohen_d = (EMA_5.5$PRE_Mean - EMA_5.5$POST_Mean) / sqrt(0.5 * (EMA_5.5$ind.pretestSD^2 + EMA_5.5$ind.posttestSD^2))

# Sollen Cohen_d %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5 = EMA_5.5 %>% 
#  within(., {Cohen_d[Cohen_d %in% c(-Inf,Inf)] = NA})

#hist(EMA_5.5$Cohen_d, col = "lightblue1", main = "EMA_5.5$Cohen_d")

cohen_d_5.5 = (mean(EMA_5.5$PRE_Mean) - mean(EMA_5.5$POST_Mean)) / sqrt(0.5 * (mean(EMA_5.5$ind.pretestSD)^2 +
  mean(EMA_5.5$ind.posttestSD)^2))

final.plot(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_POST_Mean = EMA_5.5$POST_Mean), 
           overlap(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_POST_Mean = EMA_5.5$POST_Mean))$OV)

Gepoolte Varianz zwischen Pre- und Post-Intervall-Mittelwerten in EMA_5.5 = 3.007.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten (für jede Person einzeln berechnet) in EMA_5.5 = 1.174.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten in EMA_5.5 = 1.027.

---

Cohen´s d (mit gepoolten SDs) vom Pre- zum Post-Intervall in den erweiterten Intervall-Daten (je 30 MZP)

EMA_30.30$Cohen_d = (EMA_30.30$PRE_Mean - EMA_30.30$POST_Mean) / sqrt(0.5 * (EMA_30.30$ind.pretestSD^2 + EMA_30.30$ind.posttestSD^2))

# Sollen Cohen_d %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_30.30 = EMA_30.30 %>% 
#  within(., {Cohen_d[Cohen_d %in% c(-Inf,Inf)] = NA})

#hist(EMA_30.30$Cohen_d, col = "lightblue1", main = "EMA_30.30$Cohen_d")

cohen_d_30.30 = (mean(EMA_30.30$PRE_Mean) - mean(EMA_30.30$POST_Mean)) / sqrt(0.5 * (mean(EMA_30.30$ind.pretestSD)^2 +
  mean(EMA_30.30$ind.posttestSD)^2))

final.plot(list(EMA_30.30_PRE_Mean = EMA_30.30$PRE_Mean, EMA_30.30_POST_Mean = EMA_30.30$POST_Mean), 
           overlap(list(EMA_30.30_PRE_Mean = EMA_30.30$PRE_Mean, EMA_30.30_POST_Mean = EMA_30.30$POST_Mean))$OV)

Gepoolte Varianz zwischen Pre- und Post-Intervall-Mittelwerten in EMA_30.30 = 3.007.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten (für jede Person einzeln berechnet) in EMA_30.30 = 1.291.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten in EMA_30.30 = 1.129.

---

Cohen´s d (mit gepoolten SDs) vom Pre- zum Post-Intervall in EMA_5.5_Window (je 5 MZP)

EMA_5.5_Window$Cohen_d = (EMA_5.5_Window$PRE_Mean - EMA_5.5_Window$POST_Mean) / sqrt(0.5 * (EMA_5.5_Window$ind.pretestSD^2 + EMA_5.5_Window$ind.posttestSD^2))

# Sollen Cohen_d %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Window = EMA_5.5_Window %>% 
#  within(., {Cohen_d[Cohen_d %in% c(-Inf,Inf)] = NA})

#hist(EMA_5.5_Window$Cohen_d, col = "lightblue1", main = "EMA_5.5_Window$Cohen_d")

cohen_d_5.5_Window = (mean(EMA_5.5_Window$PRE_Mean) - mean(EMA_5.5_Window$POST_Mean)) / sqrt(0.5 * (mean(EMA_5.5_Window$ind.pretestSD)^2 + mean(EMA_5.5_Window$ind.posttestSD)^2))

final.plot(list(EMA_5.5_Window_PRE_Mean = EMA_5.5_Window$PRE_Mean, EMA_5.5_Window_POST_Mean = EMA_5.5_Window$POST_Mean),
    overlap(list(EMA_5.5_Window_PRE_Mean = EMA_5.5_Window$PRE_Mean, EMA_5.5_Window_POST_Mean = EMA_5.5_Window$POST_Mean))$OV)

Gepoolte Varianz zwischen Pre- und Post-Intervall-Mittelwerten in EMA_5.5_Window = 3.256.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten (für jede Person einzeln berechnet) in EMA_5.5_Window = 1.307.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten in EMA_5.5_Window = 1.113.

---

Cohen´s d (mit gepoolten SDs) vom Pre- zum Post-Intervall in EMA_5.5_Days (je 5 MZP)

EMA_5.5_Days$Cohen_d = (EMA_5.5_Days$PRE_Mean - EMA_5.5_Days$POST_Mean) / sqrt(0.5 * (EMA_5.5_Days$ind.pretestSD^2 + EMA_5.5_Days$ind.posttestSD^2))

# Sollen Cohen_d %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Days = EMA_5.5_Days %>% 
#  within(., {Cohen_d[Cohen_d %in% c(-Inf,Inf)] = NA})

#hist(EMA_5.5_Days$Cohen_d, col = "lightblue1", main = "EMA_5.5_Days$Cohen_d")

cohen_d_5.5_Days = (mean(EMA_5.5_Days$PRE_Mean) - mean(EMA_5.5_Days$POST_Mean)) / sqrt(0.5 * (mean(EMA_5.5_Days$ind.pretestSD)^2 + mean(EMA_5.5_Days$ind.posttestSD)^2))

final.plot(list(EMA_5.5_Days_PRE_Mean = EMA_5.5_Days$PRE_Mean, EMA_5.5_Days_POST_Mean = EMA_5.5_Days$POST_Mean),
    overlap(list(EMA_5.5_Days_PRE_Mean = EMA_5.5_Days$PRE_Mean, EMA_5.5_Days_POST_Mean = EMA_5.5_Days$POST_Mean))$OV)

Gepoolte Varianz zwischen Pre- und Post-Intervall-Mittelwerten in EMA_5.5_Days = 3.513.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten (für jede Person einzeln berechnet) in EMA_5.5_Days = 1.437.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten in EMA_5.5_Days = 1.179.

---

Ab hier nur noch Vergleiche in EMA_30.30, EMA_5.5_Window und EMA_5.5_Days:

---

1.5 Klinische PHQ-9-Interpretation

PHQ_Int = tibble(PHQ_Score = c("0-4","5-9","10-14","15-19","20-27"),
       Klassifikation = c(0,1,2,3,4),
       Interpretation = c("Minimal or none","Mild","Moderate","Moderately severe","Severe"))

1.5.1 EMA_30.30

EMA_30.30 = EMA_30.30 %>% 
  mutate(PRE_Mean_klass = case_when(
    PRE_Mean <= 4 ~ 0,
    PRE_Mean > 4 & PRE_Mean < 10 ~ 1,
    PRE_Mean >= 10 & PRE_Mean < 15 ~ 2,
    PRE_Mean >= 15 & PRE_Mean < 20 ~ 3,
    PRE_Mean >= 20 ~ 4,
    TRUE ~ PRE_Mean
  )
)

temp = EMA_30.30 %>% 
  count(PRE_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(PRE_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	PRE_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	NA	NA
5-9	1	Mild	3283	40.83
10-14	2	Moderate	4732	58.86
15-19	3	Moderately severe	25	0.31
20-27	4	Severe	NA	NA

EMA_30.30 = EMA_30.30 %>% 
  mutate(POST_Mean_klass = case_when(
    POST_Mean <= 4 ~ 0,
    POST_Mean > 4 & POST_Mean < 10 ~ 1,
    POST_Mean >= 10 & POST_Mean < 15 ~ 2,
    POST_Mean >= 15 & POST_Mean < 20 ~ 3,
    POST_Mean >= 20 ~ 4,
    TRUE ~ POST_Mean
  )
)

temp = EMA_30.30 %>% 
  count(POST_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(POST_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	POST_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	862	10.72
5-9	1	Mild	6126	76.19
10-14	2	Moderate	1052	13.08
15-19	3	Moderately severe	NA	NA
20-27	4	Severe	NA	NA

temp = tibble(Classification = c(EMA_30.30$PRE_Mean_klass, EMA_30.30$POST_Mean_klass),
              Assessment = rep(as_factor(c("PRE Interval Mean", "POST Interval Mean")), each = length(EMA_30.30$PRE_Mean_klass)))#<<

temp %>%
  ggplot(aes(x = Classification, fill = Assessment)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(x = "PHQ-9 Classification", y = "")#<<

#ggsave("Plots/k20_EMA_30.30_PHQ-Class_Histogram.jpg", width = 6, height = 4)#<<

1.5.2 EMA_5.5_Window

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(PRE_Mean_klass = case_when(
    PRE_Mean <= 4 ~ 0,
    PRE_Mean > 4 & PRE_Mean < 10 ~ 1,
    PRE_Mean >= 10 & PRE_Mean < 15 ~ 2,
    PRE_Mean >= 15 & PRE_Mean < 20 ~ 3,
    PRE_Mean >= 20 ~ 4,
    TRUE ~ PRE_Mean
  )
)

temp = EMA_5.5_Window %>% 
  count(PRE_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(PRE_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	PRE_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	3	0.04
5-9	1	Mild	3316	41.24
10-14	2	Moderate	4651	57.85
15-19	3	Moderately severe	70	0.87
20-27	4	Severe	NA	NA

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(POST_Mean_klass = case_when(
    POST_Mean <= 4 ~ 0,
    POST_Mean > 4 & POST_Mean < 10 ~ 1,
    POST_Mean >= 10 & POST_Mean < 15 ~ 2,
    POST_Mean >= 15 & POST_Mean < 20 ~ 3,
    POST_Mean >= 20 ~ 4,
    TRUE ~ POST_Mean
  )
)

temp = EMA_5.5_Window %>% 
  count(POST_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(POST_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	POST_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	983	12.23
5-9	1	Mild	5842	72.66
10-14	2	Moderate	1212	15.07
15-19	3	Moderately severe	3	0.04
20-27	4	Severe	NA	NA

temp = tibble(Classification = c(EMA_5.5_Window$PRE_Mean_klass, EMA_5.5_Window$POST_Mean_klass),
              Assessment = rep(as_factor(c("PRE Interval Mean", "POST Interval Mean")), each = length(EMA_5.5_Window$PRE_Mean_klass)))#<<

temp %>%
  ggplot(aes(x = Classification, fill = Assessment)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(x = "PHQ-9 Classification", y = "")#<<

#ggsave("Plots/k20_EMA_5.5_Window_PHQ-Class_Histogram.jpg", width = 6, height = 4)#<<

1.5.3 EMA_5.5_Days

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(PRE_Mean_klass = case_when(
    PRE_Mean <= 4 ~ 0,
    PRE_Mean > 4 & PRE_Mean < 10 ~ 1,
    PRE_Mean >= 10 & PRE_Mean < 15 ~ 2,
    PRE_Mean >= 15 & PRE_Mean < 20 ~ 3,
    PRE_Mean >= 20 ~ 4,
    TRUE ~ PRE_Mean
  )
)

temp = EMA_5.5_Days %>% 
  count(PRE_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(PRE_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	PRE_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	13	0.16
5-9	1	Mild	3388	42.14
10-14	2	Moderate	4506	56.04
15-19	3	Moderately severe	133	1.65
20-27	4	Severe	NA	NA

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(POST_Mean_klass = case_when(
    POST_Mean <= 4 ~ 0,
    POST_Mean > 4 & POST_Mean < 10 ~ 1,
    POST_Mean >= 10 & POST_Mean < 15 ~ 2,
    POST_Mean >= 15 & POST_Mean < 20 ~ 3,
    POST_Mean >= 20 ~ 4,
    TRUE ~ POST_Mean
  )
)

temp = EMA_5.5_Days %>% 
  count(POST_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(POST_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	POST_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	1135	14.12
5-9	1	Mild	5562	69.18
10-14	2	Moderate	1318	16.39
15-19	3	Moderately severe	25	0.31
20-27	4	Severe	NA	NA

temp = tibble(Classification = c(EMA_5.5_Days$PRE_Mean_klass, EMA_5.5_Days$POST_Mean_klass),
              Assessment = rep(as_factor(c("PRE Interval Mean", "POST Interval Mean")), each = length(EMA_5.5_Days$PRE_Mean_klass)))#<<

temp %>%
  ggplot(aes(x = Classification, fill = Assessment)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(x = "PHQ-9 Classification", y = "")#<<

#ggsave("Plots/k20_EMA_5.5_Days_PHQ-Class_Histogram.jpg", width = 6, height = 4)#<<

---

1.6 Percentage Change (PC)

\[ PC = \Bigl(1 - \frac{\overline{x_{2}}} {\overline{x_{1}}}\Bigr) \cdot 100 \]

\(\overline{x_{2}}\) = mean of subject´s posttest scores, \(\overline{x_{1}}\) = mean of subject´s pretest scores

Interpretation des Percentage Change:

PC_Int = tibble(PC = c("PC <= -50","-50 < PC <= -25","-25 < PC < 25","25 <= PC < 50","PC >= 50"),
                Klassifikation = c(-2,-1,0,1,2),
                Interpretation = c("starke Verschlechterung","Verschlechterung","keine Veränderung",
                                   "Verbesserung","starke Verbesserung"))

1.6.1 EMA_30.30

EMA_30.30$Mean_PC = (1-(EMA_30.30$POST_Mean / EMA_30.30$PRE_Mean)) * 100

# Sollen Mean_PC %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_30.30 = EMA_30.30 %>% 
#  within(., {Mean_PC[Mean_PC %in% c(-Inf,Inf)] = NA})

EMA_30.30 = EMA_30.30 %>% 
  mutate(Mean_PC_klass = case_when(
    Mean_PC <= -50 ~ -2,
    Mean_PC > -50 & Mean_PC <= -25 ~ -1,
    Mean_PC > -25 & Mean_PC < 25 ~ 0,
    Mean_PC >= 25 & Mean_PC < 50 ~ 1,
    Mean_PC >= 50 ~ 2,
    TRUE ~ Mean_PC
  )
)


temp = EMA_30.30 %>% 
  dplyr::count(Mean_PC_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PC_Int %>%
  dplyr::rename(Mean_PC_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PC	Mean_PC_klass	Interpretation	n	Percentage
PC <= -50	-2	starke Verschlechterung	73	0.91
-50 < PC <= -25	-1	Verschlechterung	240	2.99
-25 < PC < 25	0	keine Veränderung	2919	36.31
25 <= PC < 50	1	Verbesserung	2909	36.18
PC >= 50	2	starke Verbesserung	1899	23.62

scatter.hist(EMA_30.30$PRE_Mean, EMA_30.30$Mean_PC, xlab = "EMA_30.30$PRE_Mean", ylab = "EMA_30.30$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Korrelation Mean Percentage Change (je 30 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = 0.468.

---

1.6.2 EMA_5.5_Window

EMA_5.5_Window$Mean_PC = (1-(EMA_5.5_Window$POST_Mean / EMA_5.5_Window$PRE_Mean)) * 100

# Sollen Mean_PC %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Window = EMA_5.5_Window %>% 
#  within(., {Mean_PC[Mean_PC %in% c(-Inf,Inf)] = NA})

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(Mean_PC_klass = case_when(
    Mean_PC <= -50 ~ -2,
    Mean_PC > -50 & Mean_PC <= -25 ~ -1,
    Mean_PC > -25 & Mean_PC < 25 ~ 0,
    Mean_PC >= 25 & Mean_PC < 50 ~ 1,
    Mean_PC >= 50 ~ 2,
    TRUE ~ Mean_PC
  )
)


temp = EMA_5.5_Window %>% 
  dplyr::count(Mean_PC_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PC_Int %>%
  dplyr::rename(Mean_PC_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PC	Mean_PC_klass	Interpretation	n	Percentage
PC <= -50	-2	starke Verschlechterung	123	1.53
-50 < PC <= -25	-1	Verschlechterung	313	3.89
-25 < PC < 25	0	keine Veränderung	2791	34.71
25 <= PC < 50	1	Verbesserung	2754	34.25
PC >= 50	2	starke Verbesserung	2059	25.61

scatter.hist(EMA_5.5_Window$PRE_Mean, EMA_5.5_Window$Mean_PC, xlab = "EMA_5.5_Window$PRE_Mean", ylab = "EMA_5.5_Window$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Korrelation Mean Percentage Change (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = 0.474.

---

1.6.3 EMA_5.5_Days

EMA_5.5_Days$Mean_PC = (1-(EMA_5.5_Days$POST_Mean / EMA_5.5_Days$PRE_Mean)) * 100

# Sollen Mean_PC %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Days = EMA_5.5_Days %>% 
#  within(., {Mean_PC[Mean_PC %in% c(-Inf,Inf)] = NA})

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(Mean_PC_klass = case_when(
    Mean_PC <= -50 ~ -2,
    Mean_PC > -50 & Mean_PC <= -25 ~ -1,
    Mean_PC > -25 & Mean_PC < 25 ~ 0,
    Mean_PC >= 25 & Mean_PC < 50 ~ 1,
    Mean_PC >= 50 ~ 2,
    TRUE ~ Mean_PC
  )
)


temp = EMA_5.5_Days %>% 
  dplyr::count(Mean_PC_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PC_Int %>%
  dplyr::rename(Mean_PC_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PC	Mean_PC_klass	Interpretation	n	Percentage
PC <= -50	-2	starke Verschlechterung	225	2.80
-50 < PC <= -25	-1	Verschlechterung	374	4.65
-25 < PC < 25	0	keine Veränderung	2635	32.77
25 <= PC < 50	1	Verbesserung	2550	31.72
PC >= 50	2	starke Verbesserung	2256	28.06

scatter.hist(EMA_5.5_Days$PRE_Mean, EMA_5.5_Days$Mean_PC, xlab = "EMA_5.5_Days$PRE_Mean", ylab = "EMA_5.5_Days$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Korrelation Mean Percentage Change (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = 0.494.

---

1.6.4 Zusammenhang im Scatter-Histogramm

scatter.hist(EMA_30.30$Mean_PC, EMA_5.5_Window$Mean_PC, xlab = "EMA_30.30$Mean_PC", ylab = "EMA_5.5_Window$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

scatter.hist(EMA_30.30$Mean_PC, EMA_5.5_Days$Mean_PC, xlab = "EMA_30.30$Mean_PC", ylab = "EMA_5.5_Days$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

scatter.hist(EMA_5.5_Window$Mean_PC, EMA_5.5_Days$Mean_PC, xlab = "EMA_5.5_Window$Mean_PC", ylab = "EMA_5.5_Days$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

---

1.7 Individual Reliable Change Index (ind)

1.7.1 RCI(ind) nur mit SD aus dem individuellen Pre-Intervall

\[ RCI_{ind,preSD} = \frac{\overline{x_{2}} - \overline{x_{1}}} {SE_{D,pre}} \]

\[ SE_{D,pre} = \sqrt{2 \cdot (s_{x} \cdot (1 - r_{xy})^2)} \]

\[ \text{significance cutoff} = 1.96 \cdot SE_{D,pre} = 1.96 \cdot \sqrt{2 \cdot (s_{x} \cdot (1 - r_{xy})^2)} \]

\(\overline{x_{2}}\) = mean of subject´s posttest scores, \(\overline{x_{1}}\) = mean of subject´s pretest scores, \(SE_{D,pre}\) = standard error of difference between the test scores in the individual´s pre interval \(s_{x}\) = individual standard deviation of pretest time points, \(r_{xy}\) = reliability (internal consistency Cronbach´s \(\alpha\)) of the measure, \(\text{significance cutoff}\) = (absolute) cutoff score for reliable change (95%-criterion)

EMA_30.30

EMA_30.30$SEd_pre = sqrt(2 * (EMA_30.30$ind.pretestSD * sqrt(1 - EMA_5.5_Alpha)) ^ 2)
EMA_30.30$RCI_ind_preSD = (EMA_30.30$POST_Mean - EMA_30.30$PRE_Mean) / EMA_30.30$SEd_pre
EMA_30.30$RCI_ind_preSD_Cutoff =  1.96 * EMA_30.30$SEd_pre

# Sollen SEd_pre, RCI_ind_preSD und RCI_ind_preSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_30.30 = EMA_30.30 %>% 
#  within(., {SEd_pre[SEd_pre %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD[RCI_ind_preSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD_Cutoff[RCI_ind_preSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_30.30$PRE_Mean, EMA_30.30$RCI_ind_preSD, xlab = "EMA_30.30$PRE_Mean", ylab = "EMA_30.30$RCI_ind_preSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_30.30 = 4.87.
Korrelation RCI(ind) nur mit Pre-SD (je 30 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.514.

EMA_5.5_Window

EMA_5.5_Window$SEd_pre = sqrt(2 * (EMA_5.5_Window$ind.pretestSD * sqrt(1 - EMA_5.5_Alpha)) ^ 2)
EMA_5.5_Window$RCI_ind_preSD = (EMA_5.5_Window$POST_Mean - EMA_5.5_Window$PRE_Mean) / EMA_5.5_Window$SEd_pre
EMA_5.5_Window$RCI_ind_preSD_Cutoff =  1.96 * EMA_5.5_Window$SEd_pre

# Sollen SEd_pre, RCI_ind_preSD und RCI_ind_preSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Window = EMA_5.5_Window %>% 
#  within(., {SEd_pre[SEd_pre %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD[RCI_ind_preSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD_Cutoff[RCI_ind_preSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_5.5_Window$PRE_Mean, EMA_5.5_Window$RCI_ind_preSD, xlab = "EMA_5.5_Window$PRE_Mean", ylab = "EMA_5.5_Window$RCI_ind_preSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_5.5_Window = 5.009.
Korrelation RCI(ind) nur mit Pre-SD (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.488.

EMA_5.5_Days

EMA_5.5_Days$SEd_pre = sqrt(2 * (EMA_5.5_Days$ind.pretestSD * sqrt(1 - EMA_5.5_Alpha)) ^ 2)
EMA_5.5_Days$RCI_ind_preSD = (EMA_5.5_Days$POST_Mean - EMA_5.5_Days$PRE_Mean) / EMA_5.5_Days$SEd_pre
EMA_5.5_Days$RCI_ind_preSD_Cutoff =  1.96 * EMA_5.5_Days$SEd_pre

# Sollen SEd_pre, RCI_ind_preSD und RCI_ind_preSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Days = EMA_5.5_Days %>% 
#  within(., {SEd_pre[SEd_pre %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD[RCI_ind_preSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD_Cutoff[RCI_ind_preSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_5.5_Days$PRE_Mean, EMA_5.5_Days$RCI_ind_preSD, xlab = "EMA_5.5_Days$PRE_Mean", ylab = "EMA_5.5_Days$RCI_ind_preSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_5.5_Days = 4.694.
Korrelation RCI(ind) nur mit Pre-SD (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.487.

---

1.7.2 RCI(ind) mit pooled SD aus beiden individuellen Intervallen

\[ RCI_{ind} = \frac{\overline{x_{2}} - \overline{x_{1}}} {SE_{D}} \]

\[ SE_{D} = \sqrt{(s_{x}^2 + s_{y}^2) \cdot (1 - r_{xy})} \]

\[ \text{significance cutoff} = 1.96 \cdot SE_{D} = 1.96 \cdot \sqrt{(s_{x}^2 + s_{y}^2) \cdot (1 - r_{xy})} \]

\(\overline{x_{2}}\) = mean of subject´s posttest scores, \(\overline{x_{1}}\) = mean of subject´s pretest scores, \(SE_{D}\) = pooled standard error of difference between the test scores \(s_{x}\) = individual standard deviation of pretest time points, \(s_{y}\) = individual standard deviation of pretest time points, \(r_{xy}\) = reliability (internal consistency Cronbach´s \(\alpha\)) of the measure, \(\text{significance cutoff}\) = (absolute) cutoff score for reliable change (95%-criterion)

EMA_30.30

EMA_30.30$SEd_pooled = sqrt((EMA_30.30$ind.pretestSD ^ 2 + EMA_30.30$ind.posttestSD ^ 2) * (1 - EMA_5.5_Alpha))
EMA_30.30$RCI_ind_pooledSD = (EMA_30.30$POST_Mean - EMA_30.30$PRE_Mean) / EMA_30.30$SEd_pooled
EMA_30.30$RCI_ind_pooledSD_Cutoff =  1.96 * EMA_30.30$SEd_pooled

# Sollen SEd_pooled, RCI_ind_pooledSD und RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_30.30 = EMA_30.30 %>% 
#  within(., {SEd_pooled[SEd_pooled %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD[RCI_ind_pooledSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD_Cutoff[RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_30.30$PRE_Mean, EMA_30.30$RCI_ind_pooledSD, xlab = "EMA_30.30$PRE_Mean", ylab = "EMA_30.30$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_30.30 = 5.681.
Korrelation RCI(ind) mit pooled SDs (je 30 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.481.

EMA_5.5_Window

EMA_5.5_Window$SEd_pooled = sqrt((EMA_5.5_Window$ind.pretestSD ^ 2 + EMA_5.5_Window$ind.posttestSD ^ 2) * (1 - EMA_5.5_Alpha))
EMA_5.5_Window$RCI_ind_pooledSD = (EMA_5.5_Window$POST_Mean - EMA_5.5_Window$PRE_Mean) / EMA_5.5_Window$SEd_pooled
EMA_5.5_Window$RCI_ind_pooledSD_Cutoff =  1.96 * EMA_5.5_Window$SEd_pooled

# Sollen SEd_pooled, RCI_ind_pooledSD und RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Window = EMA_5.5_Window %>% 
#  within(., {SEd_pooled[SEd_pooled %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD[RCI_ind_pooledSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD_Cutoff[RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_5.5_Window$PRE_Mean, EMA_5.5_Window$RCI_ind_pooledSD, xlab = "EMA_5.5_Window$PRE_Mean", ylab = "EMA_5.5_Window$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_5.5_Window = 5.866.
Korrelation RCI(ind) mit pooled SDs (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.469.

EMA_5.5_Days

EMA_5.5_Days$SEd_pooled = sqrt((EMA_5.5_Days$ind.pretestSD ^ 2 + EMA_5.5_Days$ind.posttestSD ^ 2) * (1 - EMA_5.5_Alpha))
EMA_5.5_Days$RCI_ind_pooledSD = (EMA_5.5_Days$POST_Mean - EMA_5.5_Days$PRE_Mean) / EMA_5.5_Days$SEd_pooled
EMA_5.5_Days$RCI_ind_pooledSD_Cutoff =  1.96 * EMA_5.5_Days$SEd_pooled

# Sollen SEd_pooled, RCI_ind_pooledSD und RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Days = EMA_5.5_Days %>% 
#  within(., {SEd_pooled[SEd_pooled %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD[RCI_ind_pooledSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD_Cutoff[RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_5.5_Days$PRE_Mean, EMA_5.5_Days$RCI_ind_pooledSD, xlab = "EMA_5.5_Days$PRE_Mean", ylab = "EMA_5.5_Days$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_5.5_Days = 5.544.
Korrelation RCI(ind) mit pooled SDs (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.476.

---

1.8 Vergleich RCI(ind) (nur Pre-SD) - RCI(ind) (pooled SDs)

scatter.hist(EMA_30.30$RCI_ind_preSD, EMA_30.30$RCI_ind_pooledSD, xlab = "EMA_30.30$RCI_ind_preSD", ylab =
               "EMA_30.30$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue",  "darkorange"))

scatter.hist(EMA_5.5_Window$RCI_ind_preSD, EMA_5.5_Window$RCI_ind_pooledSD, xlab = "EMA_5.5_Window$RCI_ind_preSD", ylab =
               "EMA_5.5_Window$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue",  "darkorange"))

scatter.hist(EMA_5.5_Days$RCI_ind_preSD, EMA_5.5_Days$RCI_ind_pooledSD, xlab = "EMA_5.5_Days$RCI_ind_preSD", ylab =
               "EMA_5.5_Days$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue",  "darkorange"))

---

1.9 RCI-Klassifikationen (= RCI + Cutoff-Krit. nach JT)

Clinically Significant Change im Sinne von Jacobson & Truax, also definiert durch einen RCI > |1.96| und die Überschreitung eines empirisch ermittelten Cutoff-Wertes, der die klinische von der gesunden Population von Testwerten trennt.

RCI_Int = tibble(RCI = c("Pre-Score >= 10 & Post-Score <= 9 & RCI < -1,96","every other combination",
                         "Pre-Score <= 9 & Post-Score >= 10 & RCI > 1,96"),
                Klassifikation = c(-1,0,1),
                Interpretation = c("reliable Verbesserung","keine reliable Veränderung","reliable Verschlechterung"))

EMA_30.30: RCI(ind) nur mit Pre-SDs

EMA_30.30 = EMA_30.30 %>% 
  mutate(RCI_ind_preSD_klass = case_when(
    #RCI_ind_preSD < -1.96 ~ -1,
    #RCI_ind_preSD >= -1.96 & RCI_ind_preSD < 1.96 ~ 0,
    #RCI_ind_preSD > 1.96 ~ 1,
    #TRUE ~ RCI_ind_preSD
    PRE_Mean >= 10 & POST_Mean <= 9 & RCI_ind_preSD < -1.96 ~ -1, #<------------- Cutoff-Kriterium hinzugefügt#
    PRE_Mean <= 9 & POST_Mean >= 10 & RCI_ind_preSD > 1.96 ~ 1,
    TRUE ~ 0
  )
)

temp = EMA_30.30 %>% 
  count(RCI_ind_preSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_preSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_preSD_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & RCI < -1,96	-1	reliable Verbesserung	2041	25.39
every other combination	0	keine reliable Veränderung	5945	73.94
Pre-Score <= 9 & Post-Score >= 10 & RCI > 1,96	1	reliable Verschlechterung	54	0.67

EMA_30.30: RCI(ind) mit pooled SDs

EMA_30.30 = EMA_30.30 %>% 
  mutate(RCI_ind_pooledSD_klass = case_when(
    #RCI_ind_pooledSD < -1.96 ~ -1,
    #RCI_ind_pooledSD >= -1.96 & RCI_ind_pooledSD < 1.96 ~ 0,
    #RCI_ind_pooledSD > 1.96 ~ 1,
    #TRUE ~ RCI_ind_pooledSD
    PRE_Mean >= 10 & POST_Mean <= 9 & RCI_ind_pooledSD < -1.96 ~ -1, #<------------- Cutoff-Kriterium hinzugefügt#
    PRE_Mean <= 9 & POST_Mean >= 10 & RCI_ind_pooledSD > 1.96 ~ 1,
    TRUE ~ 0
  )
)

temp = EMA_30.30 %>% 
  count(RCI_ind_pooledSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_pooledSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_pooledSD_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & RCI < -1,96	-1	reliable Verbesserung	1687	20.98
every other combination	0	keine reliable Veränderung	6340	78.86
Pre-Score <= 9 & Post-Score >= 10 & RCI > 1,96	1	reliable Verschlechterung	13	0.16

EMA_5.5_Window: RCI(ind) nur mit Pre-SDs

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(RCI_ind_preSD_klass = case_when(
    #RCI_ind_preSD < -1.96 ~ -1,
    #RCI_ind_preSD >= -1.96 & RCI_ind_preSD < 1.96 ~ 0,
    #RCI_ind_preSD > 1.96 ~ 1,
    #TRUE ~ RCI_ind_preSD
    PRE_Mean >= 10 & POST_Mean <= 9 & RCI_ind_preSD < -1.96 ~ -1, #<------------- Cutoff-Kriterium hinzugefügt#
    PRE_Mean <= 9 & POST_Mean >= 10 & RCI_ind_preSD > 1.96 ~ 1,
    TRUE ~ 0
  )
)

temp = EMA_5.5_Window %>% 
  count(RCI_ind_preSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_preSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_preSD_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & RCI < -1,96	-1	reliable Verbesserung	2054	25.55
every other combination	0	keine reliable Veränderung	5899	73.37
Pre-Score <= 9 & Post-Score >= 10 & RCI > 1,96	1	reliable Verschlechterung	87	1.08

EMA_5.5_Window: RCI(ind) mit pooled SDs

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(RCI_ind_pooledSD_klass = case_when(
    #RCI_ind_pooledSD < -1.96 ~ -1,
    #RCI_ind_pooledSD >= -1.96 & RCI_ind_pooledSD < 1.96 ~ 0,
    #RCI_ind_pooledSD > 1.96 ~ 1,
    #TRUE ~ RCI_ind_pooledSD
    PRE_Mean >= 10 & POST_Mean <= 9 & RCI_ind_pooledSD < -1.96 ~ -1, #<------------- Cutoff-Kriterium hinzugefügt#
    PRE_Mean <= 9 & POST_Mean >= 10 & RCI_ind_pooledSD > 1.96 ~ 1,
    TRUE ~ 0
  )
)

temp = EMA_5.5_Window %>% 
  count(RCI_ind_pooledSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_pooledSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_pooledSD_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & RCI < -1,96	-1	reliable Verbesserung	1750	21.77
every other combination	0	keine reliable Veränderung	6260	77.86
Pre-Score <= 9 & Post-Score >= 10 & RCI > 1,96	1	reliable Verschlechterung	30	0.37

EMA_5.5_Days: RCI(ind) nur mit Pre-SDs

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(RCI_ind_preSD_klass = case_when(
    #RCI_ind_preSD < -1.96 ~ -1,
    #RCI_ind_preSD >= -1.96 & RCI_ind_preSD < 1.96 ~ 0,
    #RCI_ind_preSD > 1.96 ~ 1,
    #TRUE ~ RCI_ind_preSD
    PRE_Mean >= 10 & POST_Mean <= 9 & RCI_ind_preSD < -1.96 ~ -1, #<------------- Cutoff-Kriterium hinzugefügt#
    PRE_Mean <= 9 & POST_Mean >= 10 & RCI_ind_preSD > 1.96 ~ 1,
    TRUE ~ 0
  )
)

temp = EMA_5.5_Days %>% 
  count(RCI_ind_preSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_preSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_preSD_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & RCI < -1,96	-1	reliable Verbesserung	2338	29.08
every other combination	0	keine reliable Veränderung	5550	69.03
Pre-Score <= 9 & Post-Score >= 10 & RCI > 1,96	1	reliable Verschlechterung	152	1.89

EMA_5.5_Days: RCI(ind) mit pooled SDs

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(RCI_ind_pooledSD_klass = case_when(
    #RCI_ind_pooledSD < -1.96 ~ -1,
    #RCI_ind_pooledSD >= -1.96 & RCI_ind_pooledSD < 1.96 ~ 0,
    #RCI_ind_pooledSD > 1.96 ~ 1,
    #TRUE ~ RCI_ind_pooledSD
    PRE_Mean >= 10 & POST_Mean <= 9 & RCI_ind_pooledSD < -1.96 ~ -1, #<------------- Cutoff-Kriterium hinzugefügt#
    PRE_Mean <= 9 & POST_Mean >= 10 & RCI_ind_pooledSD > 1.96 ~ 1,
    TRUE ~ 0
  )
)

temp = EMA_5.5_Days %>% 
  count(RCI_ind_pooledSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_pooledSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_pooledSD_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & RCI < -1,96	-1	reliable Verbesserung	2001	24.89
every other combination	0	keine reliable Veränderung	5965	74.19
Pre-Score <= 9 & Post-Score >= 10 & RCI > 1,96	1	reliable Verschlechterung	74	0.92

---

1.10 Edwards-Nunnally-Methode (EN) nach Speer (1992)

\[ \bigl[ r_{xx} (X_{pre} - M_{pre}) + M_{pre} \bigr] \pm 2 \cdot S_{pre} \cdot \sqrt{1 - r_{xx}} \]

\(r_{xx}\) = reliability of the measure, \(X_{pre}\) = individual´s raw score at pre-treatment, \(M_{pre}\) = mean of the sample at pre-treatment, \(S_{pre}\) = standard deviation of the sample at pre-treatment

Interpretation der Post-Ausprägung nach EN-Intervall-Methode

EN_Int = tibble(EN = c("PHQ POST < [EN-Intervall]","PHQ POST im [EN-Intervall]","PHQ POST > [EN-Intervall]"),
                Klassifikation = c(-1,0,1), Interpretation = c("signifikante Verbesserung",
                        "keine signifikante Veränderung","signifikante Verschlechterung"))

EN-Intervalle in EMA_30.30

EMA_30.30$EN_min = (EMA_5.5_Alpha * (EMA_30.30$PRE_Mean - mean(EMA_30.30$PRE_Mean)) + mean(EMA_30.30$PRE_Mean)) - 2 * mean(EMA_30.30$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_30.30$EN_max = (EMA_5.5_Alpha * (EMA_30.30$PRE_Mean - mean(EMA_30.30$PRE_Mean)) + mean(EMA_30.30$PRE_Mean)) + 2 * mean(EMA_30.30$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_30.30 = EMA_30.30 %>% 
  mutate(EN_klass = case_when(
    POST_Mean > EN_max ~ 1,
    POST_Mean <= EN_max & POST_Mean >= EN_min ~ 0,
    POST_Mean < EN_min ~ -1,
    TRUE ~ POST_Mean
  )
)

temp = EMA_30.30 %>% 
  count(EN_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

EN_Int %>%
  dplyr::rename(EN_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

EN	EN_klass	Interpretation	n	Percentage
PHQ POST < [EN-Intervall]	-1	signifikante Verbesserung	3730	46.39
PHQ POST im [EN-Intervall]	0	keine signifikante Veränderung	4293	53.40
PHQ POST > [EN-Intervall]	1	signifikante Verschlechterung	17	0.21

EN-Intervalle in EMA_5.5_Window

EMA_5.5_Window$EN_min = (EMA_5.5_Alpha * (EMA_5.5_Window$PRE_Mean - mean(EMA_5.5_Window$PRE_Mean)) + 
                           mean(EMA_5.5_Window$PRE_Mean)) - 2 *  mean(EMA_5.5_Window$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_5.5_Window$EN_max = (EMA_5.5_Alpha * (EMA_5.5_Window$PRE_Mean - mean(EMA_5.5_Window$PRE_Mean)) + 
                           mean(EMA_5.5_Window$PRE_Mean)) + 2 * mean(EMA_5.5_Window$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(EN_klass = case_when(
    POST_Mean > EN_max ~ 1,
    POST_Mean <= EN_max & POST_Mean >= EN_min ~ 0,
    POST_Mean < EN_min ~ -1,
    TRUE ~ POST_Mean
  )
)

temp = EMA_5.5_Window %>% 
  count(EN_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

EN_Int %>%
  dplyr::rename(EN_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

EN	EN_klass	Interpretation	n	Percentage
PHQ POST < [EN-Intervall]	-1	signifikante Verbesserung	3748	46.62
PHQ POST im [EN-Intervall]	0	keine signifikante Veränderung	4249	52.85
PHQ POST > [EN-Intervall]	1	signifikante Verschlechterung	43	0.53

EN-Intervalle in EMA_5.5_Days

EMA_5.5_Days$EN_min = (EMA_5.5_Alpha * (EMA_5.5_Days$PRE_Mean - mean(EMA_5.5_Days$PRE_Mean)) + 
                           mean(EMA_5.5_Days$PRE_Mean)) - 2 *  mean(EMA_5.5_Days$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_5.5_Days$EN_max = (EMA_5.5_Alpha * (EMA_5.5_Days$PRE_Mean - mean(EMA_5.5_Days$PRE_Mean)) + 
                           mean(EMA_5.5_Days$PRE_Mean)) + 2 * mean(EMA_5.5_Days$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(EN_klass = case_when(
    POST_Mean > EN_max ~ 1,
    POST_Mean <= EN_max & POST_Mean >= EN_min ~ 0,
    POST_Mean < EN_min ~ -1,
    TRUE ~ POST_Mean
  )
)

temp = EMA_5.5_Days %>% 
  count(EN_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

EN_Int %>%
  dplyr::rename(EN_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

EN	EN_klass	Interpretation	n	Percentage
PHQ POST < [EN-Intervall]	-1	signifikante Verbesserung	3993	49.66
PHQ POST im [EN-Intervall]	0	keine signifikante Veränderung	3906	48.58
PHQ POST > [EN-Intervall]	1	signifikante Verschlechterung	141	1.75

---

1.11 Clinically Significant Improvement (CSI)

Clinically Significant Improvement (CSI) vom Pre- zum Post-Intervall

“The original validation study of the PHQ-9 defined clinically significant improvement as [a pre-treatment score >= 10 and] a post-treatment score of <= 9 combined with improvement of 50%.” (McMillan, Gilbody, & Richards, 2010)

CSI_Int = tibble(CSI = c("Pre-Score >= 10 & Post-Score <= 9 & PC >= 50", "every other combination", 
                         "Pre-Score <= 9 & Post-Score >= 10 & PC <= -50"),
                Klassifikation = c(-1,0,1),
                Interpretation = c("klinisch signifikante Verbesserung", "keine klinisch signifikante Veränderung", 
                                   "klinisch signifikante Verschlechterung"))

1.11.1 CSI in EMA_30.30

EMA_30.30 = EMA_30.30 %>% 
   mutate(CSI_klass = case_when(
     PRE_Mean >= 10 & POST_Mean <= 9 & Mean_PC >= 50 ~ -1,
     PRE_Mean <= 9 & POST_Mean >= 10 & Mean_PC <= -50 ~ 1,
     TRUE ~ 0
   )
)

temp = EMA_30.30 %>% 
  count(CSI_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

CSI_Int %>%
  dplyr::rename(CSI_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

CSI	CSI_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & PC >= 50	-1	klinisch signifikante Verbesserung	1458	18.13
every other combination	0	keine klinisch signifikante Veränderung	6523	81.13
Pre-Score <= 9 & Post-Score >= 10 & PC <= -50	1	klinisch signifikante Verschlechterung	59	0.73

---

1.11.2 CSI in EMA_5.5_Window

EMA_5.5_Window = EMA_5.5_Window %>% 
   mutate(CSI_klass = case_when(
     PRE_Mean >= 10 & POST_Mean <= 9 & Mean_PC >= 50 ~ -1,
     PRE_Mean <= 9 & POST_Mean >= 10 & Mean_PC <= -50 ~ 1,
     TRUE ~ 0
   )
)

temp = EMA_5.5_Window %>% 
  count(CSI_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

CSI_Int %>%
  dplyr::rename(CSI_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

CSI	CSI_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & PC >= 50	-1	klinisch signifikante Verbesserung	1582	19.68
every other combination	0	keine klinisch signifikante Veränderung	6359	79.09
Pre-Score <= 9 & Post-Score >= 10 & PC <= -50	1	klinisch signifikante Verschlechterung	99	1.23

---

1.11.3 CSI in EMA_5.5_Days

EMA_5.5_Days = EMA_5.5_Days %>% 
   mutate(CSI_klass = case_when(
     PRE_Mean >= 10 & POST_Mean <= 9 & Mean_PC >= 50 ~ -1,
     PRE_Mean <= 9 & POST_Mean >= 10 & Mean_PC <= -50 ~ 1,
     TRUE ~ 0
   )
)

temp = EMA_5.5_Days %>% 
  count(CSI_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

CSI_Int %>%
  dplyr::rename(CSI_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

CSI	CSI_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & PC >= 50	-1	klinisch signifikante Verbesserung	1688	21.00
every other combination	0	keine klinisch signifikante Veränderung	6169	76.73
Pre-Score <= 9 & Post-Score >= 10 & PC <= -50	1	klinisch signifikante Verschlechterung	183	2.28

---

# Speichern der Datasets inkl. aller Klassifikationsvariablen ----------- nötig?
EMA_30.30_final = EMA_30.30
EMA_5.5_Window_final = EMA_5.5_Window
EMA_5.5_Days_final = EMA_5.5_Days

save(EMA_30.30_final, file = "cor_04_k20/EMA_30.30_final.RData")#<<
save(EMA_5.5_Window_final, file = "cor_04_k20/EMA_5.5_Window_final.RData")#<<
save(EMA_5.5_Days_final, file = "cor_04_k20/EMA_5.5_Days_final.RData")#<<
# Für eine Tabelle der alleinigen Klassifikationen aus allen 3 Datensets im einheitlichen Format (-1,0,1) 
# siehe die Erstellung von EMA_Class.RData unten.

1.12 Individuelle Übereinstimmung der Klassifikationen

Übereinstimmung der Klassifikationen auf individueller Ebene zwischen EMA_30.30, EMA_5.5_Window und EMA_5.5_Days

Interpretation von Cohen´s Kappa:

tibble(Cohen_Kappa = c("k < .20",".21 <= k < .40",".41 <= k < .60",".61 <= k < .80","k > .80"),
       Interpretation = c("poor","fair","moderate","good","very good")) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Cohen_Kappa	Interpretation
k < .20	poor
.21 <= k < .40	fair
.41 <= k < .60	moderate
.61 <= k < .80	good
k > .80	very good

1.12.1 Klinische PHQ-9-Interpretation

Übereinstimmung zwischen den klinischen Interpretationen der PHQ-9-Werte für Pre- und Post-Intervalle (je 30 MZP und je 5 MZP):

# PRE
x = EMA_30.30 %>% 
  select(ID, PRE_Mean_klass) %>% 
  dplyr::rename(PRE_klass_30.30 = PRE_Mean_klass)

y = EMA_5.5_Window %>% 
  select(ID, PRE_Mean_klass) %>% 
  dplyr::rename(PRE_klass_5.5_Window = PRE_Mean_klass)

z = EMA_5.5_Days %>% 
  select(ID, PRE_Mean_klass) %>% 
  dplyr::rename(PRE_klass_5.5_Days = PRE_Mean_klass)

temp = full_join(x, y, by = "ID") %>% 
  full_join(., z, by = "ID") %>% 
  select(-ID) %>% 
  mutate(across(.cols = everything(), as.factor))

### Cohen´s Kappa
rnames = c("PRE_klass_30.30", "PRE_klass_5.5_Window", "PRE_klass_5.5_Days")

Agreement = matrix(ncol = 3, nrow = 3, dimnames = list(rnames, rnames))

for (i in 1:nrow(Agreement)) {
  for (j in 1:ncol(Agreement)) {
    x = eval(parse(text = paste0("temp$", names(temp[,i]))))
    y = eval(parse(text = paste0("temp$", names(temp[,j]))))
    
    Agreement[i,j] = CohenKappa(x = x, y = y)
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Agreement, col = heat.colors(n=5, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.7, cex = 0.8, las = 2, 
     key = list(cex.axis=0.7), ann = FALSE, breaks = c(0, 0.21, 0.41, 0.61, 0.81, 1));
  title(main = "Übereinstimmung (Cohen´s Kappa) der PHQ-PRE-Klassifikationen")

# POST
x = EMA_30.30 %>% 
  select(ID, POST_Mean_klass) %>% 
  dplyr::rename(POST_klass_30.30 = POST_Mean_klass)

y = EMA_5.5_Window %>% 
  select(ID, POST_Mean_klass) %>% 
  dplyr::rename(POST_klass_5.5_Window = POST_Mean_klass)

z = EMA_5.5_Days %>% 
  select(ID, POST_Mean_klass) %>% 
  dplyr::rename(POST_klass_5.5_Days = POST_Mean_klass)

temp = full_join(x, y, by = "ID") %>% 
  full_join(., z, by = "ID") %>% 
  select(-ID) %>% 
  mutate(across(.cols = everything(), as.factor))

### Cohen´s Kappa
rnames = c("POST_klass_30.30", "POST_klass_5.5_Window", "POST_klass_5.5_Days")

Agreement = matrix(ncol = 3, nrow = 3, dimnames = list(rnames, rnames))

for (i in 1:nrow(Agreement)) {
  for (j in 1:ncol(Agreement)) {
    x = eval(parse(text = paste0("temp$", names(temp[,i]))))
    y = eval(parse(text = paste0("temp$", names(temp[,j]))))
    
    Agreement[i,j] = CohenKappa(x = x, y = y)
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Agreement, col = heat.colors(n=5, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.7, cex = 0.8, las = 2, 
     key = list(cex.axis=0.7), ann = FALSE, breaks = c(0, 0.21, 0.41, 0.61, 0.81, 1));
  title(main = "Übereinstimmung (Cohen´s Kappa) der PHQ-POST-Klassifikationen")

---

1.12.2 Zusammenfassung der Klassifikations-Häufigkeiten

# einheitliche Kodierung von Verbesserung (-1), keiner Veränderung (0) und Verschlechterung (1):

x = EMA_30.30 %>% 
  select(ID, Mean_PC_klass, RCI_ind_preSD_klass, RCI_ind_pooledSD_klass, EN_klass, CSI_klass) %>% 
  dplyr::rename(Mean_PC_30.30 = Mean_PC_klass, RCI_ind_preSD_30.30 = RCI_ind_preSD_klass, 
         RCI_ind_pooledSD_30.30 = RCI_ind_pooledSD_klass, EN_30.30 = EN_klass, CSI_30.30 = CSI_klass) %>% 
  mutate(Mean_PC_30.30 = recode(Mean_PC_30.30, '-2' = 1L, '-1' = 0L, '0' = 0L, '1' = 0L, '2' = -1L))

y = EMA_5.5_Window %>% 
  select(ID, Mean_PC_klass, RCI_ind_preSD_klass, RCI_ind_pooledSD_klass, EN_klass, CSI_klass) %>% 
  dplyr::rename(Mean_PC_5.5_Window = Mean_PC_klass, RCI_ind_preSD_5.5_Window = RCI_ind_preSD_klass, 
         RCI_ind_pooledSD_5.5_Window = RCI_ind_pooledSD_klass, EN_5.5_Window = EN_klass, CSI_5.5_Window = CSI_klass) %>% 
  mutate(Mean_PC_5.5_Window = recode(Mean_PC_5.5_Window, '-2' = 1L, '-1' = 0L, '0' = 0L, '1' = 0L, '2' = -1L))

z = EMA_5.5_Days %>% 
  select(ID, Mean_PC_klass, RCI_ind_preSD_klass, RCI_ind_pooledSD_klass, EN_klass, CSI_klass) %>% 
  dplyr::rename(Mean_PC_5.5_Days = Mean_PC_klass, RCI_ind_preSD_5.5_Days = RCI_ind_preSD_klass, 
         RCI_ind_pooledSD_5.5_Days = RCI_ind_pooledSD_klass, EN_5.5_Days = EN_klass, CSI_5.5_Days = CSI_klass) %>% 
  mutate(Mean_PC_5.5_Days = recode(Mean_PC_5.5_Days, '-2' = 1L, '-1' = 0L, '0' = 0L, '1' = 0L, '2' = -1L))

EMA_Class = full_join(x, y, by = "ID") %>% 
  full_join(., z, "ID") %>% 
  select(-ID) %>% 
  dplyr::mutate(across(.cols = everything(), as.factor))
#save(EMA_Class, file = "cor_04_k20/EMA_Class.RData")

rnames = names(EMA_Class)

#view(dfSummary(EMA_Class))
#dfSummary(EMA_Class, plain.ascii = FALSE, style = 'grid', graph.magnif = 0.75, valid.col = FALSE, tmp.img.dir = "/tmp")
#dfSummary(EMA_Class)
print(dfSummary(EMA_Class, varnumbers = FALSE, plain.ascii = FALSE, style = 'grid', graph.magnif = 0.75, valid.col = FALSE, na.col = FALSE, display.labels = FALSE, silent = FALSE, headers = FALSE, footnote = NA, tmp.img.dir = "/tmp"), method = 'render')

Data Frame Summary

EMA_Class

Dimensions: 8040 x 15
Duplicates: 7370

Variable	Stats / Values	Freqs (% of Valid)	Graph
Mean_PC_30.30 [factor]	1. -1 2. 0 3. 1	1899 ( 23.6% ) 6068 ( 75.5% ) 73 ( 0.9% )
RCI_ind_preSD_30.30 [factor]	1. -1 2. 0 3. 1	2041 ( 25.4% ) 5945 ( 73.9% ) 54 ( 0.7% )
RCI_ind_pooledSD_30.30 [factor]	1. -1 2. 0 3. 1	1687 ( 21.0% ) 6340 ( 78.9% ) 13 ( 0.2% )
EN_30.30 [factor]	1. -1 2. 0 3. 1	3730 ( 46.4% ) 4293 ( 53.4% ) 17 ( 0.2% )
CSI_30.30 [factor]	1. -1 2. 0 3. 1	1458 ( 18.1% ) 6523 ( 81.1% ) 59 ( 0.7% )
Mean_PC_5.5_Window [factor]	1. -1 2. 0 3. 1	2059 ( 25.6% ) 5858 ( 72.9% ) 123 ( 1.5% )
RCI_ind_preSD_5.5_Window [factor]	1. -1 2. 0 3. 1	2054 ( 25.5% ) 5899 ( 73.4% ) 87 ( 1.1% )
RCI_ind_pooledSD_5.5_Window [factor]	1. -1 2. 0 3. 1	1750 ( 21.8% ) 6260 ( 77.9% ) 30 ( 0.4% )
EN_5.5_Window [factor]	1. -1 2. 0 3. 1	3748 ( 46.6% ) 4249 ( 52.8% ) 43 ( 0.5% )
CSI_5.5_Window [factor]	1. -1 2. 0 3. 1	1582 ( 19.7% ) 6359 ( 79.1% ) 99 ( 1.2% )
Mean_PC_5.5_Days [factor]	1. -1 2. 0 3. 1	2256 ( 28.1% ) 5559 ( 69.1% ) 225 ( 2.8% )
RCI_ind_preSD_5.5_Days [factor]	1. -1 2. 0 3. 1	2338 ( 29.1% ) 5550 ( 69.0% ) 152 ( 1.9% )
RCI_ind_pooledSD_5.5_Days [factor]	1. -1 2. 0 3. 1	2001 ( 24.9% ) 5965 ( 74.2% ) 74 ( 0.9% )
EN_5.5_Days [factor]	1. -1 2. 0 3. 1	3993 ( 49.7% ) 3906 ( 48.6% ) 141 ( 1.8% )
CSI_5.5_Days [factor]	1. -1 2. 0 3. 1	1688 ( 21.0% ) 6169 ( 76.7% ) 183 ( 2.3% )

Generated by summarytools 0.9.8 (R version 4.0.2)
2021-08-20

---

1.12.3 Übereinstimmung der Klassifikations-Häufigkeiten

Gesamt-Übereinstimmung

### Cohen´s Kappa
Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Agreement)) {
  for (j in 1:ncol(Agreement)) {
    x = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,i]))))
    y = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,j]))))
    
    Agreement[i,j] = CohenKappa(x = x, y = y)
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Agreement, col = heat.colors(n=5, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.21, 0.41, 0.61, 0.81, 1));
  title(main = "Übereinstimmung (Cohen´s Kappa) der Klassifikationen")

### Prozentuale Übereinstimmung
Percentage_Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Percentage_Agreement)) {
  for (j in 1:ncol(Percentage_Agreement)) {
    x = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,i]))))
    y = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,j]))))
    
    Percentage_Agreement[i,j] = Agree(cbind(x, y))[1]
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Percentage_Agreement, col = heat.colors(n=4, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.26, 0.51, 0.76, 1));
  title(main = "Prozentuale Übereinstimmung der Klassifikationen")

Übereinstimmung nur für Verbesserung (-1)

### Cohen´s Kappa
Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Agreement)) {
  for (j in 1:ncol(Agreement)) {
    x = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,i])))) %>% 
      dplyr::recode_factor(., '-1' = -1L)
    y = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,j])))) %>% 
      dplyr::recode_factor(., '-1' = -1L)
    
    Agreement[i,j] = CohenKappa(x = x, y = y, useNA = "ifany")
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Agreement, col = heat.colors(n=5, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.21, 0.41, 0.61, 0.81, 1));
  title(main = "Übereinstimmung (Cohen´s Kappa): Verbesserung (-1)")

### Prozentuale Übereinstimmung
Percentage_Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Percentage_Agreement)) {
  for (j in 1:ncol(Percentage_Agreement)) {
    x = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,i]))))
    y = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,j]))))
    
    Percentage_Agreement[i,j] = length(which(x == -1L & y == -1L)) / 
      length(which(x == -1L | y == -1L))
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Percentage_Agreement, col = heat.colors(n=4, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.26, 0.51, 0.76, 1));
  title(main = "Prozentuale Übereinstimmung: Verbesserung (-1)")

Übereinstimmung nur für Verschlechterung (1)

### Cohen´s Kappa
Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Agreement)) {
  for (j in 1:ncol(Agreement)) {
    x = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,i])))) %>% 
      recode_factor(., '1' = 1L)
    y = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,j])))) %>% 
      recode_factor(., '1' = 1L)
    
    Agreement[i,j] = CohenKappa(x = x, y = y, useNA = "ifany")
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Agreement, col = heat.colors(n=5, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.21, 0.41, 0.61, 0.81, 1));
  title(main = "Übereinstimmung (Cohen´s Kappa): Verschlechterung (1)")

### Prozentuale Übereinstimmung
Percentage_Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Percentage_Agreement)) {
  for (j in 1:ncol(Percentage_Agreement)) {
    x = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,i]))))
    y = eval(parse(text = paste0("EMA_Class$", names(EMA_Class[,j]))))
    
    Percentage_Agreement[i,j] = length(which(x == 1L & y == 1L)) / 
      length(which(x == 1L | y == 1L))
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Percentage_Agreement, col = heat.colors(n=4, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.26, 0.51, 0.76, 1));
  title(main = "Prozentuale Übereinstimmung: Verschlechterung (1)")

---

1.13 Sensitivität und Spezifität der Klassifikationsmethoden

Diagnostische Sensitivität und Spezifität einer “neuen” Testmethode im Vergleich zu einer “Goldstandard”-Testmethode:
Sensitivität = Wahrscheinlichkeit für ein richtig-positives Testergebnis
Spezifität = Wahrscheinlichkeit für ein richtig-negatives Testergebnis

\[ Sensitivity = Recall = TPR = \frac{\sum{\text{True Positives}}} {\sum{\text{True Positives}} + \sum{\text{False Negatives}}} = \frac{tp}{tp + fn} \]

\[ Specificity = Selectivity = TNR = \frac{\sum{\text{True Negatives}}} {\sum{\text{True Negatives}} + \sum{\text{False Positives}}} = \frac{tn}{tn + fp} \]

\[ \textit{Geometric Mean of Sensitivity and Specificity} = \sqrt{Sensitivity \cdot Specificity} \]

\[ Sensitivity_{\textit{class-weighted average}} = Recall_{wgt} = \rho_{wgt} = \sum_{k=1}^{c} \frac{n_k}{n} \rho_k = \frac{1}{n} \sum_{k=1}^{c} tp^{(k)} = \frac{tp^{(deteriorated)}} {tp^{(deteriorated)} + fn^{(deteriorated)}} + \frac{tp^{(\textit{not changed})}} {tp^{(\textit{not changed})} + fn^{(\textit{not changed})}} + \frac{tp^{(improved)}} {tp^{(improved)} + fn^{(improved)}} \]

\(c\) = number of classes (i.e. 3: deteriorated; not changed; improved); \(n_k\) = number of cases belonging to class \(k\), with \(k=1,...,c\); \(n\) = total number of cases, with \(n = \sum_{k=1}^{c} n_k\)

Sensitivität & Spezifität gegenüber Veränderung:
Evaluation der Veränderungs-Klassifikationen der Klassifikationsmethoden im Vergleich zur klinischen Signifikanz CSI (je 30 MZP) als “Goldstandard”:

ClassEval = list()
for (i in 1:ncol(EMA_Class)) {
  x = eval(parse(text = paste0("EMA_Class$", colnames(EMA_Class[,i]))))
  cm = confusionMatrix(x, reference = EMA_Class$CSI_30.30, 
                       dnn = c(paste0("EMA_Class$", names(EMA_Class[,i])), "CSI 30.30"), mode = "everything")
  cm$agreement = cm$overall[c("Accuracy","Kappa")]
  cm$senspez = cm$byClass %>% 
    as_tibble() %>% 
    select(Sensitivity, Specificity)
  
  cm$senspez_cwa = cm$senspez %>% 
    summarise(across(.cols = everything(), .fns = geometric.mean, .names = "{.col}_cwa")) %>% 
    mutate(GMean_SenSpez = geometric.mean(c(Sensitivity_cwa, Specificity_cwa)))
  
  ClassEval[[paste0(names(EMA_Class[,i]))]] = cm[c("table","agreement","senspez","senspez_cwa")]
}

#save(ClassEval, file = "cor_04_k20/EMA_ClassEval.RData")
#load("cor_04_k20/EMA_Class.RData")

SenSpezSumm = tibble(Frequency = as.factor(c(rep("30.30", 5), rep("5.5", 10))),
                 Method = colnames(EMA_Class),
                 Sens_imp = as.numeric(NA),
                 Sens_not = as.numeric(NA),
                 Sens_det = as.numeric(NA),
                 Spec_imp = as.numeric(NA),
                 Spec_not = as.numeric(NA),
                 Spec_det = as.numeric(NA),
                 Sensitivity_cwa = as.numeric(NA),
                 Specificity_cwa = as.numeric(NA),
                 SenSpec_mean = as.numeric(NA),
                 Accuracy_PercAgree = as.numeric(NA),
                 Kappa = as.numeric(NA))

for (i in 1:nrow(SenSpezSumm)) {
  SenSpezSumm[i,"Sens_imp"] = ClassEval[[i]][["senspez"]]$Sensitivity[1]
  SenSpezSumm[i,"Sens_not"] = ClassEval[[i]][["senspez"]]$Sensitivity[2]
  SenSpezSumm[i,"Sens_det"] = ClassEval[[i]][["senspez"]]$Sensitivity[3]
  
  SenSpezSumm[i,"Spec_imp"] = ClassEval[[i]][["senspez"]]$Specificity[1]
  SenSpezSumm[i,"Spec_not"] = ClassEval[[i]][["senspez"]]$Specificity[2]
  SenSpezSumm[i,"Spec_det"] = ClassEval[[i]][["senspez"]]$Specificity[3]
  
  SenSpezSumm[i,"Sensitivity_cwa"] = ClassEval[[i]][["senspez_cwa"]]$Sensitivity_cwa
  SenSpezSumm[i,"Specificity_cwa"] = ClassEval[[i]][["senspez_cwa"]]$Specificity_cwa
  SenSpezSumm[i,"SenSpec_mean"] = ClassEval[[i]][["senspez_cwa"]]$GMean_SenSpez
  
  SenSpezSumm[i,"Accuracy_PercAgree"] = ClassEval[[i]][["agreement"]][[1]]
  SenSpezSumm[i,"Kappa"] = ClassEval[[i]][["agreement"]][[2]]
}

#save(SenSpezSumm, file = "cor_04_k20/EMA_SenSpezSumm.RData")
#load("cor_04_k20/EMA_SenSpezSumm.RData")

SenSpezSumm %>% 
  mutate(across(.cols = where(is.numeric), .fns = round, digits = 2)) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Frequency	Method	Sens_imp	Sens_not	Sens_det	Spec_imp	Spec_not	Spec_det	Sensitivity_cwa	Specificity_cwa	SenSpec_mean	Accuracy_PercAgree	Kappa
30.30	Mean_PC_30.30	1.00	0.93	1.00	0.93	1.00	1.00	0.98	0.98	0.98	0.94	0.84
30.30	RCI_ind_preSD_30.30	0.84	0.87	0.47	0.88	0.83	1.00	0.70	0.90	0.79	0.86	0.61
30.30	RCI_ind_pooledSD_30.30	0.88	0.94	0.17	0.94	0.85	1.00	0.52	0.93	0.69	0.92	0.75
30.30	EN_30.30	1.00	0.65	0.25	0.65	0.97	1.00	0.55	0.86	0.69	0.71	0.40
30.30	CSI_30.30	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
5.5	Mean_PC_5.5_Window	0.86	0.86	0.69	0.88	0.85	0.99	0.80	0.90	0.85	0.86	0.62
5.5	RCI_ind_preSD_5.5_Window	0.74	0.84	0.49	0.85	0.73	0.99	0.67	0.85	0.76	0.82	0.50
5.5	RCI_ind_pooledSD_5.5_Window	0.76	0.90	0.15	0.90	0.74	1.00	0.47	0.87	0.64	0.87	0.60
5.5	EN_5.5_Window	0.98	0.64	0.20	0.65	0.95	1.00	0.50	0.85	0.65	0.70	0.38
5.5	CSI_5.5_Window	0.81	0.93	0.69	0.94	0.80	0.99	0.80	0.91	0.85	0.91	0.71
5.5	Mean_PC_5.5_Days	0.83	0.81	0.81	0.84	0.83	0.98	0.82	0.88	0.85	0.82	0.53
5.5	RCI_ind_preSD_5.5_Days	0.76	0.79	0.56	0.81	0.75	0.99	0.70	0.84	0.77	0.78	0.44
5.5	RCI_ind_pooledSD_5.5_Days	0.76	0.86	0.37	0.86	0.75	0.99	0.62	0.86	0.73	0.84	0.53
5.5	EN_5.5_Days	0.97	0.59	0.53	0.61	0.95	0.99	0.67	0.83	0.75	0.66	0.34
5.5	CSI_5.5_Days	0.77	0.89	0.75	0.91	0.76	0.98	0.80	0.88	0.84	0.87	0.61

SenSpezSumm %>% 
  ggplot(aes(x = Method, weight = Sensitivity_cwa)) + 
  geom_bar(fill = "#0c4c8a") + 
  coord_flip() + 
  theme_bw() + 
  labs(y = "Sensitivity to Change (Reference = CSI_30.30)")#<<
#ggsave("Plots/k20_EMA_Sensitivity_Barplot.jpg", width = 6, height = 4)#<<

SenSpezSumm %>% 
  ggplot(aes(x = Method, weight = Specificity_cwa)) + 
  geom_bar(fill = "#0c4c8a") + 
  coord_flip() + 
  theme_bw() + 
  labs(y = "Specificity to Change (Reference = CSI_30.30)")#<<
#ggsave("Plots/k20_EMA_Specificity_Barplot.jpg", width = 6, height = 4)#<<

SenSpezSumm %>% 
  ggplot(aes(x = Method, weight = SenSpec_mean)) + 
  geom_bar(fill = "#0c4c8a") + 
  coord_flip() + 
  theme_bw() + 
  labs(y = "Mean of Sensitivity and Specificity (Reference = CSI_30.30)")#<<
#ggsave("Plots/k20_EMA_SenSpec-Mean_Barplot.jpg", width = 6, height = 4)#<<

SenSpezSumm %>% 
  ggplot(aes(x = Method, weight = Accuracy_PercAgree)) + 
  geom_bar(fill = "#0c4c8a") + 
  coord_flip() + 
  theme_bw() + 
  labs(y = "Accuracy = Percentage Agreement (Reference = CSI_30.30)")#<<
#ggsave("Plots/k20_EMA_PercAgree_Barplot.jpg", width = 6, height = 4)#<<

SenSpezSumm %>% 
  ggplot(aes(x = Method, weight = Kappa)) + 
  geom_bar(fill = "#0c4c8a") + 
  coord_flip() + 
  theme_bw() + 
  labs(y = "Agreement: Cohen´s Kappa (Reference = CSI_30.30)")#<<
#ggsave("Plots/k20_EMA_Kappa_Barplot.jpg", width = 6, height = 4)#<<



df = SenSpezSumm %>% 
  pivot_longer(cols = Sens_imp:Kappa, names_to = "Index", values_to = "Estimate") %>% 
  mutate(Method = as_factor(Method), Index = as_factor(Index))#<<

#ggplot(df) +
# aes(x = Method, colour = Index, weight = Estimate) +
# geom_bar(position = "dodge", fill = "#0c4c8a") +
# scale_color_hue() +
# theme_gray()#<<
#ggsave("Plots/k20_EMA_Class_Evaluation_by_Methods.jpg", width = 6, height = 4)#<<

---

Sensitivität & Spezifität gegenüber Veränderung:
Evaluation der Veränderungs-Klassifikationen der Klassifikationsmethoden within-method, between-frequencies, jeweils mit den Klassifikationen der Methode im 30-MZP-Szenario als Referenz:

#load("cor_04_k20/EMA_Class.RData")

########## Agreement between Mean PCs in 30-fold, 5-fold Random Window and 5-fold Random Days assessment frequencies
EMA_Class_PC = EMA_Class %>% select(Mean_PC_30.30,Mean_PC_5.5_Window,Mean_PC_5.5_Days)
ClassEval_PC = list()
for (i in 1:ncol(EMA_Class_PC)) {
  x = eval(parse(text = paste0("EMA_Class_PC$", colnames(EMA_Class_PC[,i]))))
  cm = confusionMatrix(x, reference = EMA_Class_PC$Mean_PC_30.30, 
                       dnn = c(paste0("EMA_Class_PC$", names(EMA_Class_PC[,i])), "Mean PC 30.30"), mode = "everything")
  cm$agreement = cm$overall[c("Accuracy","Kappa")]
  cm$senspez = cm$byClass %>% 
    as_tibble() %>% 
    select(Sensitivity, Specificity)
  
  cm$senspez_cwa = cm$senspez %>% 
    summarise(across(.cols = everything(), .fns = geometric.mean, .names = "{.col}_cwa")) %>% 
    mutate(GMean_SenSpez = geometric.mean(c(Sensitivity_cwa, Specificity_cwa)))
  
  ClassEval_PC[[paste0(names(EMA_Class_PC[,i]))]] = cm[c("table","agreement","senspez","senspez_cwa")]
}

#save(ClassEval_PC, file = "cor_04_k20/EMA_ClassEval_PC.RData")
#load("cor_04_k20/EMA_ClassEval_PC.RData")

SenSpezSumm_PC = tibble(Frequency = as.factor(c("30.30","5.5 Window","5.5 Days")),
                 Method = colnames(EMA_Class_PC),
                 Sens_imp = as.numeric(NA),
                 Sens_not = as.numeric(NA),
                 Sens_det = as.numeric(NA),
                 Spec_imp = as.numeric(NA),
                 Spec_not = as.numeric(NA),
                 Spec_det = as.numeric(NA),
                 Sensitivity_cwa = as.numeric(NA),
                 Specificity_cwa = as.numeric(NA),
                 SenSpec_mean = as.numeric(NA),
                 Accuracy_PercAgree = as.numeric(NA),
                 Kappa = as.numeric(NA))

for (i in 1:nrow(SenSpezSumm_PC)) {
  SenSpezSumm_PC[i,"Sens_imp"] = ClassEval_PC[[i]][["senspez"]]$Sensitivity[1]
  SenSpezSumm_PC[i,"Sens_not"] = ClassEval_PC[[i]][["senspez"]]$Sensitivity[2]
  SenSpezSumm_PC[i,"Sens_det"] = ClassEval_PC[[i]][["senspez"]]$Sensitivity[3]
  
  SenSpezSumm_PC[i,"Spec_imp"] = ClassEval_PC[[i]][["senspez"]]$Specificity[1]
  SenSpezSumm_PC[i,"Spec_not"] = ClassEval_PC[[i]][["senspez"]]$Specificity[2]
  SenSpezSumm_PC[i,"Spec_det"] = ClassEval_PC[[i]][["senspez"]]$Specificity[3]
  
  SenSpezSumm_PC[i,"Sensitivity_cwa"] = ClassEval_PC[[i]][["senspez_cwa"]]$Sensitivity_cwa
  SenSpezSumm_PC[i,"Specificity_cwa"] = ClassEval_PC[[i]][["senspez_cwa"]]$Specificity_cwa
  SenSpezSumm_PC[i,"SenSpec_mean"] = ClassEval_PC[[i]][["senspez_cwa"]]$GMean_SenSpez
  
  SenSpezSumm_PC[i,"Accuracy_PercAgree"] = ClassEval_PC[[i]][["agreement"]][[1]]
  SenSpezSumm_PC[i,"Kappa"] = ClassEval_PC[[i]][["agreement"]][[2]]
}

#save(SenSpezSumm_PC, file = "cor_04_k20/EMA_SenSpezSumm_PC.RData")
#load("cor_04_k20/EMA_SenSpezSumm_PC.RData")

SenSpezSumm_PC %>% 
  mutate(across(.cols = where(is.numeric), .fns = round, digits = 2)) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Frequency	Method	Sens_imp	Sens_not	Sens_det	Spec_imp	Spec_not	Spec_det	Sensitivity_cwa	Specificity_cwa	SenSpec_mean	Accuracy_PercAgree	Kappa
30.30	Mean_PC_30.30	1.00	1.00	1.0	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
5.5 Window	Mean_PC_5.5_Window	0.86	0.92	0.7	0.93	0.85	0.99	0.82	0.92	0.87	0.90	0.74
5.5 Days	Mean_PC_5.5_Days	0.83	0.86	0.7	0.89	0.83	0.98	0.79	0.90	0.84	0.85	0.64

########## Agreement between CSI(PC)s in 30-fold, 5-fold Random Window and 5-fold Random Days assessment frequencies
EMA_Class_CSI = EMA_Class %>% select(CSI_30.30,CSI_5.5_Window,CSI_5.5_Days)
ClassEval_CSI = list()
for (i in 1:ncol(EMA_Class_CSI)) {
  x = eval(parse(text = paste0("EMA_Class_CSI$", colnames(EMA_Class_CSI[,i]))))
  cm = confusionMatrix(x, reference = EMA_Class_CSI$CSI_30.30, 
                       dnn = c(paste0("EMA_Class_CSI$", names(EMA_Class_CSI[,i])), "CSI Mean PC 30.30"), mode = "everything")
  cm$agreement = cm$overall[c("Accuracy","Kappa")]
  cm$senspez = cm$byClass %>% 
    as_tibble() %>% 
    select(Sensitivity, Specificity)
  
  cm$senspez_cwa = cm$senspez %>% 
    summarise(across(.cols = everything(), .fns = geometric.mean, .names = "{.col}_cwa")) %>% 
    mutate(GMean_SenSpez = geometric.mean(c(Sensitivity_cwa, Specificity_cwa)))
  
  ClassEval_CSI[[paste0(names(EMA_Class_CSI[,i]))]] = cm[c("table","agreement","senspez","senspez_cwa")]
}

#save(ClassEval_CSI, file = "cor_04_k20/EMA_ClassEval_CSI.RData")
#load("cor_04_k20/EMA_ClassEval_CSI.RData")

SenSpezSumm_CSI = tibble(Frequency = as.factor(c("30.30","5.5 Window","5.5 Days")),
                 Method = colnames(EMA_Class_CSI),
                 Sens_imp = as.numeric(NA),
                 Sens_not = as.numeric(NA),
                 Sens_det = as.numeric(NA),
                 Spec_imp = as.numeric(NA),
                 Spec_not = as.numeric(NA),
                 Spec_det = as.numeric(NA),
                 Sensitivity_cwa = as.numeric(NA),
                 Specificity_cwa = as.numeric(NA),
                 SenSpec_mean = as.numeric(NA),
                 Accuracy_PercAgree = as.numeric(NA),
                 Kappa = as.numeric(NA))

for (i in 1:nrow(SenSpezSumm_CSI)) {
  SenSpezSumm_CSI[i,"Sens_imp"] = ClassEval_CSI[[i]][["senspez"]]$Sensitivity[1]
  SenSpezSumm_CSI[i,"Sens_not"] = ClassEval_CSI[[i]][["senspez"]]$Sensitivity[2]
  SenSpezSumm_CSI[i,"Sens_det"] = ClassEval_CSI[[i]][["senspez"]]$Sensitivity[3]
  
  SenSpezSumm_CSI[i,"Spec_imp"] = ClassEval_CSI[[i]][["senspez"]]$Specificity[1]
  SenSpezSumm_CSI[i,"Spec_not"] = ClassEval_CSI[[i]][["senspez"]]$Specificity[2]
  SenSpezSumm_CSI[i,"Spec_det"] = ClassEval_CSI[[i]][["senspez"]]$Specificity[3]
  
  SenSpezSumm_CSI[i,"Sensitivity_cwa"] = ClassEval_CSI[[i]][["senspez_cwa"]]$Sensitivity_cwa
  SenSpezSumm_CSI[i,"Specificity_cwa"] = ClassEval_CSI[[i]][["senspez_cwa"]]$Specificity_cwa
  SenSpezSumm_CSI[i,"SenSpec_mean"] = ClassEval_CSI[[i]][["senspez_cwa"]]$GMean_SenSpez
  
  SenSpezSumm_CSI[i,"Accuracy_PercAgree"] = ClassEval_CSI[[i]][["agreement"]][[1]]
  SenSpezSumm_CSI[i,"Kappa"] = ClassEval_CSI[[i]][["agreement"]][[2]]
}

#save(SenSpezSumm_CSI, file = "cor_04_k20/EMA_SenSpezSumm_CSI.RData")
#load("cor_04_k20/EMA_SenSpezSumm_CSI.RData")

SenSpezSumm_CSI %>% 
  mutate(across(.cols = where(is.numeric), .fns = round, digits = 2)) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Frequency	Method	Sens_imp	Sens_not	Sens_det	Spec_imp	Spec_not	Spec_det	Sensitivity_cwa	Specificity_cwa	SenSpec_mean	Accuracy_PercAgree	Kappa
30.30	CSI_30.30	1.00	1.00	1.00	1.00	1.00	1.00	1.0	1.00	1.00	1.00	1.00
5.5 Window	CSI_5.5_Window	0.81	0.93	0.69	0.94	0.80	0.99	0.8	0.91	0.85	0.91	0.71
5.5 Days	CSI_5.5_Days	0.77	0.89	0.75	0.91	0.76	0.98	0.8	0.88	0.84	0.87	0.61

########## Agreement between RCIs (ind.) in 30-fold, 5-fold Random Window and 5-fold Random Days assessment frequencies
EMA_Class_RCI = EMA_Class %>% select(RCI_ind_preSD_30.30,RCI_ind_preSD_5.5_Window,RCI_ind_preSD_5.5_Days)
ClassEval_RCI = list()
for (i in 1:ncol(EMA_Class_RCI)) {
  x = eval(parse(text = paste0("EMA_Class_RCI$", colnames(EMA_Class_RCI[,i]))))
  cm = confusionMatrix(x, reference = EMA_Class_RCI$RCI_ind_preSD_30.30, 
                       dnn = c(paste0("EMA_Class_RCI$", names(EMA_Class_RCI[,i])), "RCI ind pre-SD 30.30"), mode = "everything")
  cm$agreement = cm$overall[c("Accuracy","Kappa")]
  cm$senspez = cm$byClass %>% 
    as_tibble() %>% 
    select(Sensitivity, Specificity)
  
  cm$senspez_cwa = cm$senspez %>% 
    summarise(across(.cols = everything(), .fns = geometric.mean, .names = "{.col}_cwa")) %>% 
    mutate(GMean_SenSpez = geometric.mean(c(Sensitivity_cwa, Specificity_cwa)))
  
  ClassEval_RCI[[paste0(names(EMA_Class_RCI[,i]))]] = cm[c("table","agreement","senspez","senspez_cwa")]
}

#save(ClassEval_RCI, file = "cor_04_k20/EMA_ClassEval_RCI.RData")
#load("cor_04_k20/EMA_ClassEval_RCI.RData")

SenSpezSumm_RCI = tibble(Frequency = as.factor(c("30.30","5.5 Window","5.5 Days")),
                 Method = colnames(EMA_Class_RCI),
                 Sens_imp = as.numeric(NA),
                 Sens_not = as.numeric(NA),
                 Sens_det = as.numeric(NA),
                 Spec_imp = as.numeric(NA),
                 Spec_not = as.numeric(NA),
                 Spec_det = as.numeric(NA),
                 Sensitivity_cwa = as.numeric(NA),
                 Specificity_cwa = as.numeric(NA),
                 SenSpec_mean = as.numeric(NA),
                 Accuracy_PercAgree = as.numeric(NA),
                 Kappa = as.numeric(NA))

for (i in 1:nrow(SenSpezSumm_RCI)) {
  SenSpezSumm_RCI[i,"Sens_imp"] = ClassEval_RCI[[i]][["senspez"]]$Sensitivity[1]
  SenSpezSumm_RCI[i,"Sens_not"] = ClassEval_RCI[[i]][["senspez"]]$Sensitivity[2]
  SenSpezSumm_RCI[i,"Sens_det"] = ClassEval_RCI[[i]][["senspez"]]$Sensitivity[3]
  
  SenSpezSumm_RCI[i,"Spec_imp"] = ClassEval_RCI[[i]][["senspez"]]$Specificity[1]
  SenSpezSumm_RCI[i,"Spec_not"] = ClassEval_RCI[[i]][["senspez"]]$Specificity[2]
  SenSpezSumm_RCI[i,"Spec_det"] = ClassEval_RCI[[i]][["senspez"]]$Specificity[3]
  
  SenSpezSumm_RCI[i,"Sensitivity_cwa"] = ClassEval_RCI[[i]][["senspez_cwa"]]$Sensitivity_cwa
  SenSpezSumm_RCI[i,"Specificity_cwa"] = ClassEval_RCI[[i]][["senspez_cwa"]]$Specificity_cwa
  SenSpezSumm_RCI[i,"SenSpec_mean"] = ClassEval_RCI[[i]][["senspez_cwa"]]$GMean_SenSpez
  
  SenSpezSumm_RCI[i,"Accuracy_PercAgree"] = ClassEval_RCI[[i]][["agreement"]][[1]]
  SenSpezSumm_RCI[i,"Kappa"] = ClassEval_RCI[[i]][["agreement"]][[2]]
}

#save(SenSpezSumm_RCI, file = "cor_04_k20/EMA_SenSpezSumm_RCI.RData")
#load("cor_04_k20/EMA_SenSpezSumm_RCI.RData")

SenSpezSumm_RCI %>% 
  mutate(across(.cols = where(is.numeric), .fns = round, digits = 2)) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Frequency	Method	Sens_imp	Sens_not	Sens_det	Spec_imp	Spec_not	Spec_det	Sensitivity_cwa	Specificity_cwa	SenSpec_mean	Accuracy_PercAgree	Kappa
30.30	RCI_ind_preSD_30.30	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
5.5 Window	RCI_ind_preSD_5.5_Window	0.80	0.92	0.74	0.93	0.80	0.99	0.82	0.90	0.86	0.89	0.72
5.5 Days	RCI_ind_preSD_5.5_Days	0.79	0.86	0.63	0.88	0.79	0.99	0.75	0.88	0.81	0.84	0.61

---

1.14 Jackknife-Methode zum Resampling von Messzeitpunkten

Statt wenige zufällige MZP-Kombinationen zu ziehen und diese dann mit den “wahren” Schätzwerten und Klassifikationen (= berechnet anhand der gesamten Intervalle mit je 30 MZP) zu vergleichen, sollen die empirische Verteilung der Parameter und somit der Schätzfehler über Resampling-Methoden wie Jackknife-Verfahren und Bootstrapping berechnet werden.

Percentage Change (PC)

###### EMA_30.30
n = 30

Mean_PC = function(x, ID_df) {(1-((mean(ID_df[x,2])) / (mean(ID_df[x,1])))) * 100}

for (i in 1:nrow(EMA_30.30)) {
  df = data.frame(PRE = as.numeric(EMA_30.30[i,pre_30mzp]), POST = as.numeric(EMA_30.30[i,post_30mzp]))
  
  EMA_30.30[i,"Mean_PC_jse"] = jackknife(1:n, Mean_PC, df)$jack.se
  EMA_30.30[i,"Mean_PC_jbias"] = jackknife(1:n, Mean_PC, df)$jack.bias
  message(i)
}

EMA_30.30_Mean_PC_JK = EMA_30.30 %>% 
  select(ID, Mean_PC_jse, Mean_PC_jbias)
save(EMA_30.30_Mean_PC_JK, file = "Jackknife/EMA_30.30_Mean_PC_JK_k20.RData")

###### EMA_5.5_Window
n = 5

Mean_PC = function(x, ID_df) {(1-((mean(ID_df[x,2])) / (mean(ID_df[x,1])))) * 100}

for (i in 1:nrow(EMA_5.5_Window)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Window[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Window[i,post_5mzp]))
  
  EMA_5.5_Window[i,"Mean_PC_jse"] = jackknife(1:n, Mean_PC, df)$jack.se
  EMA_5.5_Window[i,"Mean_PC_jbias"] = jackknife(1:n, Mean_PC, df)$jack.bias
  message(i)
}

EMA_5.5_Window_Mean_PC_JK = EMA_5.5_Window %>% 
  select(ID, Mean_PC_jse, Mean_PC_jbias)
save(EMA_5.5_Window_Mean_PC_JK, file = "Jackknife/EMA_5.5_Window_Mean_PC_JK_k20.RData")

###### EMA_5.5_Days
n = 5

Mean_PC = function(x, ID_df) {(1-((mean(ID_df[x,2])) / (mean(ID_df[x,1])))) * 100}

for (i in 1:nrow(EMA_5.5_Days)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Days[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Days[i,post_5mzp]))
  
  EMA_5.5_Days[i,"Mean_PC_jse"] = jackknife(1:n, Mean_PC, df)$jack.se
  EMA_5.5_Days[i,"Mean_PC_jbias"] = jackknife(1:n, Mean_PC, df)$jack.bias
  message(i)
}

EMA_5.5_Days_Mean_PC_JK = EMA_5.5_Days %>% 
  select(ID, Mean_PC_jse, Mean_PC_jbias)
save(EMA_5.5_Days_Mean_PC_JK, file = "Jackknife/EMA_5.5_Days_Mean_PC_JK_k20.RData")

load("Jackknife/EMA_30.30_Mean_PC_JK_k20.RData")
load("Jackknife/EMA_5.5_Window_Mean_PC_JK_k20.RData")
load("Jackknife/EMA_5.5_Days_Mean_PC_JK_k20.RData")

EMA_30.30 = full_join(EMA_30.30, EMA_30.30_Mean_PC_JK, by = "ID")
EMA_5.5_Window = full_join(EMA_5.5_Window, EMA_5.5_Window_Mean_PC_JK, by = "ID")
EMA_5.5_Days = full_join(EMA_5.5_Days, EMA_5.5_Days_Mean_PC_JK, by = "ID")

temp = tibble(Jackknife_SE = c(EMA_30.30$Mean_PC_jse, EMA_5.5_Window$Mean_PC_jse, EMA_5.5_Days$Mean_PC_jse),
              Datasets = as_factor(rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each = length(EMA_30.30$Mean_PC_jse))))#<<

temp %>%
  ggplot(aes(x = Jackknife_SE, fill = Datasets)) +
  geom_histogram(alpha = 0.2, position = "identity") +
  labs(x = "Jackknife SE of Mean Percentage Change", y = "Cases") +
  theme_gray()#<<

#ggsave("Plots/k20_EMA_Mean_PC_JK_SE.jpg", width = 6, height = 4)#<<

temp %>% 
  ggplot(aes(x = Datasets, y = Jackknife_SE)) +
  geom_boxplot(fill = "dodgerblue", na.rm = TRUE, outlier.size = 1) +
  labs(x = "Dataset", y = "Jackknife SE of Mean Percentage Change") +
  theme_gray()#<<

#ggsave("Plots/k20_EMA_Mean_PC_JK_SE_Box.jpg", width = 6, height = 4)#<<


temp = tibble(Jackknife_Bias = c(EMA_30.30$Mean_PC_jbias, EMA_5.5_Window$Mean_PC_jbias, EMA_5.5_Days$Mean_PC_jbias),
              Datasets = as_factor(rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each = length(EMA_30.30$Mean_PC_jbias))))#<<

temp %>%
  ggplot(aes(x = Jackknife_Bias, fill = Datasets)) +
  geom_histogram(alpha = 0.2, position = "identity") +
  labs(x = "Jackknife Bias of Mean Percentage Change", y = "Cases") +
  theme_gray()#<<

#ggsave("Plots/k20_EMA_Mean_PC_JK_Bias.jpg", width = 6, height = 4)#<<

#temp %>% 
#  ggplot(aes(x = Datasets, y = Jackknife_Bias)) +
#  geom_boxplot(fill = "dodgerblue", na.rm = TRUE, outlier.size = 1) +
#  labs(x = "Dataset", y = "Jackknife Bias of Mean Percentage Change") +
#  theme_gray()#<<
#ggsave("Plots/k20_EMA_Mean_PC_JK_Bias_Box.jpg", width = 6, height = 4)#<<

RCI(ind) nur mit SD aus dem individuellen Pre-Intervall

###### EMA_30.30
n = 30

RCI_ind_preSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt(2 * (sd(ID_df[x,1]) * sqrt(1 - EMA_5.5_Alpha))^2)}

for (i in 1:nrow(EMA_30.30)) {
  df = data.frame(PRE = as.numeric(EMA_30.30[i,pre_30mzp]), POST = as.numeric(EMA_30.30[i,post_30mzp]))
  
  EMA_30.30[i,"RCI_ind_preSD_jse"] = jackknife(1:n, RCI_ind_preSD, df)$jack.se
  EMA_30.30[i,"RCI_ind_preSD_jbias"] = jackknife(1:n, RCI_ind_preSD, df)$jack.bias
  message(i)
}

EMA_30.30_RCI_ind_preSD_JK = EMA_30.30 %>% 
  select(ID, RCI_ind_preSD_jse, RCI_ind_preSD_jbias)
save(EMA_30.30_RCI_ind_preSD_JK, file = "Jackknife/EMA_30.30_RCI_ind_preSD_JK_k20.RData")

###### EMA_5.5_Window
n = 5

RCI_ind_preSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt(2 * (sd(ID_df[x,1]) * sqrt(1 - EMA_5.5_Alpha))^2)}

for (i in 1:nrow(EMA_5.5_Window)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Window[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Window[i,post_5mzp]))
  
  EMA_5.5_Window[i,"RCI_ind_preSD_jse"] = jackknife(1:n, RCI_ind_preSD, df)$jack.se
  EMA_5.5_Window[i,"RCI_ind_preSD_jbias"] = jackknife(1:n, RCI_ind_preSD, df)$jack.bias
  message(i)
}

EMA_5.5_Window_RCI_ind_preSD_JK = EMA_5.5_Window %>% 
  select(ID, RCI_ind_preSD_jse, RCI_ind_preSD_jbias)
save(EMA_5.5_Window_RCI_ind_preSD_JK, file = "Jackknife/EMA_5.5_Window_RCI_ind_preSD_JK_k20.RData")

###### EMA_5.5_Days
n = 5

RCI_ind_preSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt(2 * (sd(ID_df[x,1]) * sqrt(1 - EMA_5.5_Alpha))^2)}

for (i in 1:nrow(EMA_5.5_Days)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Days[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Days[i,post_5mzp]))
  
  EMA_5.5_Days[i,"RCI_ind_preSD_jse"] = jackknife(1:n, RCI_ind_preSD, df)$jack.se
  EMA_5.5_Days[i,"RCI_ind_preSD_jbias"] = jackknife(1:n, RCI_ind_preSD, df)$jack.bias
  message(i)
}

EMA_5.5_Days_RCI_ind_preSD_JK = EMA_5.5_Days %>% 
  select(ID, RCI_ind_preSD_jse, RCI_ind_preSD_jbias)
save(EMA_5.5_Days_RCI_ind_preSD_JK, file = "Jackknife/EMA_5.5_Days_RCI_ind_preSD_JK_k20.RData")

load("Jackknife/EMA_30.30_RCI_ind_preSD_JK_k20.RData")
load("Jackknife/EMA_5.5_Window_RCI_ind_preSD_JK_k20.RData")
load("Jackknife/EMA_5.5_Days_RCI_ind_preSD_JK_k20.RData")

EMA_30.30 = full_join(EMA_30.30, EMA_30.30_RCI_ind_preSD_JK, by = "ID")
EMA_5.5_Window = full_join(EMA_5.5_Window, EMA_5.5_Window_RCI_ind_preSD_JK, by = "ID")
EMA_5.5_Days = full_join(EMA_5.5_Days, EMA_5.5_Days_RCI_ind_preSD_JK, by = "ID")

temp = tibble(Jackknife_SE = c(EMA_30.30$RCI_ind_preSD_jse, EMA_5.5_Window$RCI_ind_preSD_jse, EMA_5.5_Days$RCI_ind_preSD_jse),
              Datasets = as_factor(rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each = length(EMA_30.30$RCI_ind_preSD_jse))))#<<

temp %>%
  ggplot(aes(x = Jackknife_SE, fill = Datasets)) +
  geom_histogram(alpha = 0.2, position = "identity") +
  labs(x = "Jackknife SE of RCI(ind) With Pre-SDs", y = "Cases") +
  theme_gray()#<<

#ggsave("Plots/k20_EMA_RCI_ind_preSD_JK_SE.jpg", width = 6, height = 4)#<<

temp %>% 
  ggplot(aes(x = Datasets, y = Jackknife_SE)) +
  geom_boxplot(fill = "dodgerblue", na.rm = TRUE, outlier.size = 1) +
  labs(x = "Dataset", y = "Jackknife SE of RCI(ind) With Pre-SDs") +
  theme_gray()#<<

#ggsave("Plots/k20_EMA_RCI_ind_preSD_JK_SE_Box.jpg", width = 6, height = 4)#<<


temp = tibble(Jackknife_Bias = c(EMA_30.30$RCI_ind_preSD_jbias, EMA_5.5_Window$RCI_ind_preSD_jbias,
                                 EMA_5.5_Days$RCI_ind_preSD_jbias),
              Datasets = as_factor(rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), 
                                       each = length(EMA_30.30$RCI_ind_preSD_jbias))))#<<

temp %>%
  ggplot(aes(x = Jackknife_Bias, fill = Datasets)) +
  geom_histogram(alpha = 0.2, position = "identity") +
  labs(x = "Jackknife Bias of RCI(ind) With Pre-SDs", y = "Cases") +
  theme_gray()#<<

#ggsave("Plots/k20_EMA_RCI_ind_preSD_JK_Bias.jpg", width = 6, height = 4)#<<

#temp %>% 
#  ggplot(aes(x = Datasets, y = Jackknife_Bias)) +
#  geom_boxplot(fill = "dodgerblue", na.rm = TRUE, outlier.size = 1) +
#  labs(x = "Dataset", y = "Jackknife Bias of RCI(ind) With Pre-SDs") +
#  theme_gray()#<<
#ggsave("Plots/k20_EMA_RCI_ind_preSD_JK_Bias_Box.jpg", width = 6, height = 4)#<<

RCI(ind) mit pooled SDs aus beiden individuellen Intervallen

###### EMA_30.30
n = 30

RCI_ind_pooledSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt((sd(ID_df[x,1])^ 2 + sd(ID_df[x,2])^ 2) * (1 - EMA_5.5_Alpha))}

for (i in 1:nrow(EMA_30.30)) {
  df = data.frame(PRE = as.numeric(EMA_30.30[i,pre_30mzp]), POST = as.numeric(EMA_30.30[i,post_30mzp]))
  
  EMA_30.30[i,"RCI_ind_pooledSD_jse"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.se
  EMA_30.30[i,"RCI_ind_pooledSD_jbias"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.bias
  message(i)
}

EMA_30.30_RCI_ind_pooledSD_JK = EMA_30.30 %>% 
  select(ID, RCI_ind_pooledSD_jse, RCI_ind_pooledSD_jbias)
save(EMA_30.30_RCI_ind_pooledSD_JK, file = "Jackknife/EMA_30.30_RCI_ind_pooledSD_JK_k20.RData")

###### EMA_5.5_Window
n = 5

RCI_ind_pooledSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt((sd(ID_df[x,1])^ 2 + sd(ID_df[x,2])^ 2) * (1 - EMA_5.5_Alpha))}

for (i in 1:nrow(EMA_5.5_Window)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Window[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Window[i,post_5mzp]))
  
  EMA_5.5_Window[i,"RCI_ind_pooledSD_jse"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.se
  EMA_5.5_Window[i,"RCI_ind_pooledSD_jbias"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.bias
  message(i)
}

EMA_5.5_Window_RCI_ind_pooledSD_JK = EMA_5.5_Window %>% 
  select(ID, RCI_ind_pooledSD_jse, RCI_ind_pooledSD_jbias)
save(EMA_5.5_Window_RCI_ind_pooledSD_JK, file = "Jackknife/EMA_5.5_Window_RCI_ind_pooledSD_JK_k20.RData")

###### EMA_5.5_Days
n = 5

RCI_ind_pooledSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt((sd(ID_df[x,1])^ 2 + sd(ID_df[x,2])^ 2) * (1 - EMA_5.5_Alpha))}

for (i in 1:nrow(EMA_5.5_Days)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Days[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Days[i,post_5mzp]))
  
  EMA_5.5_Days[i,"RCI_ind_pooledSD_jse"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.se
  EMA_5.5_Days[i,"RCI_ind_pooledSD_jbias"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.bias
  message(i)
}

EMA_5.5_Days_RCI_ind_pooledSD_JK = EMA_5.5_Days %>% 
  select(ID, RCI_ind_pooledSD_jse, RCI_ind_pooledSD_jbias)
save(EMA_5.5_Days_RCI_ind_pooledSD_JK, file = "Jackknife/EMA_5.5_Days_RCI_ind_pooledSD_JK_k20.RData")

load("Jackknife/EMA_30.30_RCI_ind_pooledSD_JK_k20.RData")
load("Jackknife/EMA_5.5_Window_RCI_ind_pooledSD_JK_k20.RData")
load("Jackknife/EMA_5.5_Days_RCI_ind_pooledSD_JK_k20.RData")

EMA_30.30 = full_join(EMA_30.30, EMA_30.30_RCI_ind_pooledSD_JK, by = "ID")
EMA_5.5_Window = full_join(EMA_5.5_Window, EMA_5.5_Window_RCI_ind_pooledSD_JK, by = "ID")
EMA_5.5_Days = full_join(EMA_5.5_Days, EMA_5.5_Days_RCI_ind_pooledSD_JK, by = "ID")

temp = tibble(Jackknife_SE = c(EMA_30.30$RCI_ind_pooledSD_jse, EMA_5.5_Window$RCI_ind_pooledSD_jse,
                               EMA_5.5_Days$RCI_ind_pooledSD_jse),
              Datasets = as_factor(rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), 
                                       each = length(EMA_30.30$RCI_ind_pooledSD_jse))))#<<

temp %>%
  ggplot(aes(x = Jackknife_SE, fill = Datasets)) +
  geom_histogram(alpha = 0.2, position = "identity") +
  labs(x = "Jackknife SE of RCI(ind) With Pooled SDs", y = "Cases") +
  theme_gray()#<<

#ggsave("Plots/k20_EMA_RCI_ind_pooledSD_JK_SE.jpg", width = 6, height = 4)#<<

temp %>% 
  ggplot(aes(x = Datasets, y = Jackknife_SE)) +
  geom_boxplot(fill = "dodgerblue", na.rm = TRUE, outlier.size = 1) +
  labs(x = "Dataset", y = "Jackknife SE of RCI(ind) With Pooled SDs") +
  theme_gray()#<<

#ggsave("Plots/k20_EMA_RCI_ind_pooledSD_JK_SE_Box.jpg", width = 6, height = 4)#<<


temp = tibble(Jackknife_Bias = c(EMA_30.30$RCI_ind_pooledSD_jbias, EMA_5.5_Window$RCI_ind_pooledSD_jbias,
                               EMA_5.5_Days$RCI_ind_pooledSD_jbias),
              Datasets = as_factor(rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), 
                                       each = length(EMA_30.30$RCI_ind_pooledSD_jbias))))#<<

temp %>%
  ggplot(aes(x = Jackknife_Bias, fill = Datasets)) +
  geom_histogram(alpha = 0.2, position = "identity") +
  labs(x = "Jackknife Bias of RCI(ind) With Pooled SDs", y = "Cases") +
  theme_gray()#<<

#ggsave("Plots/k20_EMA_RCI_ind_pooledSD_JK_Bias.jpg", width = 6, height = 4)#<<

#temp %>% 
#  ggplot(aes(x = Datasets, y = Jackknife_Bias)) +
#  geom_boxplot(fill = "dodgerblue", na.rm = TRUE, outlier.size = 1) +
#  labs(x = "Dataset", y = "Jackknife Bias of RCI(ind) With Pooled SDs") +
#  theme_gray()#<<
#ggsave("Plots/k20_EMA_RCI_ind_pooledSD_JK_Bias_Box.jpg", width = 6, height = 4)#<<

---